No, such a restriction is not effective. The Supremacy Clause of the Constitution, and other sections as well, provides otherwise. This was settled early on in the history of US Jurisprudence
In Fletcher v. Peck, 10 U.S. (6 Cranch) 87 (1810) Justice Johnson wrote for the majority at 10 U. S. 136 (et seq) and 10 U. S. 139:
The validity of this rescinding act, then, might well be doubted, were Georgia a single sovereign power. But Georgia cannot be viewed as a single, unconnected, sovereign power, on whose legislature no other restrictions are imposed than may be found in its own Constitution. She is a part of a large empire; she is a member of the American Union; and that Union has a Constitution the supremacy of which all acknowledge, and which imposes limits to the legislatures of the several States which none claim a right to pass ...
It is, then, the unanimous opinion of the Court that, in this case, the estate having passed into the hands of a purchaser for a valuable consideration, without notice, the State of Georgia was restrained, either by general principles which are common to our free institutions or by the particular provisions of the Constitution of the United States, from passing a law whereby the estate of the plaintiff in the premises so purchased could be constitutionally and legally impaired and rendered null and void.
(See also the Wikipedia article on the case
The court this case (for the first time in US history) held a state law unconstitutional, and nothing in the ruling suggested that this was a unique power of the Supreme Court: rather it was and is a power, in proper cases, of every general Federal court, whether a District Court, a Circuit Court of Appeals, or the Supreme Court. Indeed in Fletcher v. Peck, the Supreme court in the passage just quoted was upholding a district court decision to the same effect, thus clearly indicating that the power to strike down state laws as contrary to the Federal Constitution is found at the district court level.
In the case of Martin v. Hunter's Lessee, 14 U.S. (1 Wheat.) 304 (1816) Justice Story wrote for the Court (at 14 U. S. 328 et seq):
The third article of the Constitution is that which must principally attract our attention. The 1st. section declares,
The judicial power of the United States shall be vested in one Supreme Court, and in such other inferior Courts as the Congress may, from time to time, ordain and establish.
The 2d section declares, that
The judicial power shall extend to all cases in law or equity, arising under this Constitution, the laws of the United States, and the treaties made, or which shall be made, under their authority; to all cases affecting ambassadors, other public ministers and consuls; to all cases of admiralty and maritime jurisdiction; to controversies to which the United States shall be a party; to controversies between two or more States; between a State and citizens of another State; between citizens of different States; between citizens of the same State, claiming lands under the grants of different States; and between a State or the citizens thereof, and foreign States, citizens, or subjects.
It then proceeds to declare, that
in all cases affecting ambassadors, other public ministers and consuls, and those in which a State shall be a party, the Supreme Court shall have original jurisdiction. In all the other cases before mentioned, the Supreme Court shall have appellate jurisdiction both as to law and fact, with such exceptions and under such regulations, as the Congress shall make.
Such is the language of the article creating and defining the judicial power of the United States. It is the voice of the whole American people solemnly declared, in establishing one great department of that Government which was, in many respects, national, and in all, supreme. It is a part of the very same instrument which was to act not merely upon individuals, but upon States, and to deprive them altogether of the exercise of some powers of sovereignty and to restrain and regulate them in the exercise of others.
... it is manifest that the judicial power of the
United States is unavoidably, in some cases, exclusive of all State authority, and in all others, may be made so at the election of Congress. ...
... The exercise of appellate jurisdiction is far from being limited by the terms of the Constitution to the Supreme Court. There can be no doubt that Congress may create a succession of inferior tribunals, in each of which it may vest appellate as well as original jurisdiction. The judicial power is delegated by the Constitution in the most general terms, and may therefore be exercised by Congress under every variety of form of appellate or original jurisdiction. And as there is nothing in the Constitution which restrains or limits this power, it must therefore, in all other cases, subsist in the utmost latitude of which, in its own nature, it is susceptible.
As, then, by the terms of the Constitution, the appellate jurisdiction is not limited as to the Supreme Court, and as to this Court it may be exercised in all other cases than those of which it has original cognizance, what is there to restrain its exercise over State tribunals in the enumerated cases? The appellate power is not limited by the terms of the third article to any particular Courts. The words are, "the judicial power (which includes appellate power) shall extend to all cases," &c., and "in all other cases before mentioned, the Supreme Court shall have appellate jurisdiction." It is the case, then, and not the court, that gives the jurisdiction. If the judicial power extends to the case, it will be in vain to search in the letter of the Constitution for any qualification as to the tribunal where it depends. ...
(See also the Wikipedia article on the case
This case makes it particularly clear that the "judicial power of the United States" extends to all general federal courts (as opposed to limited courts such as the Tax Court or the Court of Claims). If the Supreme Court can make a given ruling, so can any district or circuit court (aside from the limited class of cases where the Supreme court has original jurisdiction). Rulings by lower courts may be taken to the Supreme Court, but are binding until and unless overruled or modified by a higher court. A state may not validly hold in one of its laws that it will obey a judgement by the Supreme Court, but not by a lower Federal court that has proper jurisdiction of the case.
I have quoted these two early cases from the Marshall Court because this is a matter that was settled early, and rarely if ever disputed afterwards.