You would think so, but no
While at first glance, President Trump sending a staff member to testify under oath in his place (to nullify any personal risk of perjury?) appears to epitomize the concept of "hearsay"--
a statement that:
(1) the declarant does not make while testifying at the current trial or hearing; and
(2) a party offers in evidence to prove the truth of the matter asserted in the statement
--there are some subtle but important distinctions and exceptions in play. I'm going to list them off in increasing order of relevance.
FOIA penalties are civil, not criminal
The official DOJ website lists off the penalties for Freedom of Information Act violations:
The court may award reasonable attorney fees and other litigation costs against the government when the complainant substantially prevails. See 5 U.S.C. Sec. 552(a)(4)(E).
Action Against Individual Employees: Sanctions may be taken against individual agency employees who are found to have acted arbitrarily or capriciously in improperly withholding records. Additionally, the court must award attorney fees and other litigation costs against the government.
When the statutory requirements are found by the Court to have been met, the Merit Systems Protection Board (MSPB) must promptly initiate a proceeding to determine whether disciplinary action is warranted against the office or employee who is primarily responsible for the withholding. The MSPB, after investigating and considering the evidence, submits its findings and recommendations to the agency concerned which then is required to take the corrective action recommended by the Board. See 5 U.S.C. Sec. 552(a)(4)(F). Additionally, there now exists independent jurisdiction for such MSPB investigations under 5 U.S.C. Sec. 1206(e)(1) (1982).
Failure to comply with a court order to produce the records in question may also result in punishment for contempt for the responsible employee. See 5 U.S.C. Sec. 552(a)(4)(G).
So the strongest penalty against any individual government official who violated FOIA would be losing their job, or civil contempt of court. In principle the prohibition against hearsay applies equally to civil cases as criminal ones; in practice, because the stakes are lower, courts may take a somewhat looser attitude towards hearsay in civil cases than they would in a similar criminal case.
Rule 807(a), "Residual Exceptions"
Rule 807(a) gives courts large latitude to determine whether or not to admit hearsay evidence:
(a) In General. Under the following conditions, a hearsay statement is not excluded by the rule against hearsay even if the statement is not admissible under a hearsay exception in Rule 803 or 804:
(1) the statement is supported by sufficient guarantees of trustworthiness–after considering the totality of circumstances under which it was made and evidence, if any, corroborating the statement; and
(2) it is more probative on the point for which it is offered than any other evidence that the proponent can obtain through reasonable efforts.
In this situation, the presiding judge, Reggie Walton of the D.C. District Court, clarified what he would consider "sufficient guarantees of trustworthiness":
U.S. District Court Judge Reggie Walton issued the rare order to the White House last week after expressing dissatisfaction with a previous explanation submitted by the Justice Department’s top career official, Associate Deputy Attorney General Bradley Weinsheimer. Weinsheimer said he had checked with an unidentified official in the White House counsel’s office and determined that no new declassification was triggered by Trump’s latest tweets.
However, Walton said given Trump’s suggestions of a rogue element undercutting his orders, some assurance directly from the president or someone who had spoken to the president was necessary.
As Meadows had, one presumes, literally spoken to the president, this satisfied the presiding judge's own explicit standard of "sufficient guarantees of trustworthiness" for when hearsay may be admitted into evidence.
Rule 807(a)(2) is also relevant here, in its caveat that hearsay may be accepted into evidence when it is "more probative...than any other evidence that the proponent can obtain through reasonable efforts". Arguably, forcing the POTUS to neglect his duties running the country and "ending the pandemic" long enough to testify in what is, in many ways, a run-of-the-mill FOIA case, would take too much effort to be "reasonable". Which brings me to the next point:
Rule 804(a)(1) and Rule 804(b)(5), "Unavailability of the Declarant"
Rule 804(a)(1) discusses a specific exception to the hearsay rule when the declarant can't or won't personally testify:
(a) Criteria for Being Unavailable. A declarant is considered to be unavailable as a witness if the declarant:
(1) is exempted from testifying about the subject matter of the declarant’s statement because the court rules that a privilege applies
As POTUS, it makes sense that Trump would have some degree of privilege or immunity from being deposed. If a sitting President could be dragged into court at will over any government litigation, no matter how mundane, to personally testify, it would be impossible to perform the functions of their office.
Think about all of the live issues winding their way through the courts right now that Trump has tweeted about. Now, imagine the demands on his time if he was dragged into court to testify regarding every single one: "Sorry Angela Merkel, I have to cancel our international summit this year, I'm giving a live deposition in 50 different court cases in the next three weeks and I don't have time to do 'foreign policy' right now. Hope no new World Wars break out! Good luck!"
Of necessity, a POTUS has to be permitted to delegate 99.9% of legal representation on matters of public policy to other Executive Branch officials, when it comes to who actually needs to be physically present in court. And since he is privileged from personally testifying, that means exception 804(b)(5) applies:
(b) The Exceptions. The following are not excluded by the rule against hearsay if the declarant is unavailable as a witness:
(5) [Other Exceptions .] [Transferred to Rule 807.]
We discussed how Rule 807 applies in this circumstance up above. But I want to circle back to the idea that the President has to be able to delegate statements of official policy to other authorized government representatives, such as Meadows, because of the clinching exception:
Rule 803(8)(A)(i): Public records of governmental policy aren't excluded by the hearsay rule
Rule 803(8)(A)(i) tells us that:
statements of public policy (such as, whether the government is going to declassify, or has already declassified, every document relating to the Russia investigation, specifically including Mueller report and FBI interview redactions)
made by public offices or their official representatives (such as
the POTUS's chief of staff, authorized to speak on behalf of the
POTUS, clarifying the Executive Branch's stance on declassification)
are not excluded by the hearsay rule:
The following are not excluded by the rule against hearsay, regardless of whether the declarant is available as a witness:
(8) Public Records. A record or statement of a public office if:
(A) it sets out:
(i) the office’s activities
This makes sense given the purpose of the rule against hearsay. It's supposed to prevent innuendo and rumor from sneaking into the factual record when the facts are in dispute: "I heard the defendant's mom say the defendant said he did it," related by the defendant's mom's bingo buddy, would deservedly raise some eyebrows around the bingo table, but isn't the kind of solid evidence an impartial trial requires.
Statements of public policy and government action by public officials, on the other hand, have a lot more authority and credibility than what a friend of a friend of the defendant heard the friend say the defendant said. Meadows isn't (just) some random golf buddy of the President who overheard what the President was thinking when he made these tweets; he's the President's official delegate to the court, conveying the Executive Branch's official position on declassification. Such official statements are ordinarily presumed maximally trustworthy and reliable, at least partly for logistical reasons. Similar to how we can't ask Trump to cancel all the COVID task force meetings to clear his schedule and testify about some tweets, we can't drag every government officer who makes an out-of-court official public statement or record into court to certify it--at least, not every single time. The judicial branch of the government takes the word of other branches of the government mostly at face value†, and does not consider public records or statements in an official capacity as "hearsay" to be excluded from evidence.
So the TL;DR version is:
No, Meadows coming into court to convey this statement on behalf of his boss would not be excluded by the hearsay rule.
†Significantly, statements or records regarding policy might be excluded as hearsay, per 803(8)(B), if the opposition demonstrates that the statement or record is somehow fishy or unreliable: "(B) the opponent does not show that the source of information or other circumstances indicate a lack of trustworthiness." But in this instance, in order to demonstrate a "lack of trustworthiness", the plaintiffs in the case--BuzzFeed, CNN, and the Electronic Privacy Information Center--would have to show that the government was actually declassifying and unredacting all material related to the Russia investigation, contrary to what Meadows claimed in court. Since the government is not actually doing this, the President's social media rants notwithstanding, the plaintiffs would be unlikely to prevail if they tried to use 803(8)(B) to get Meadows' testimony excluded as hearsay.