Nobody says you have to wait until the deadline runs.
Filing a notice of appeal shouldn't waive the right to remove either.
Probably the safest course of action is to file a notice of appeal both before and after the removal to avoid any risk of losing the right to appeal the interlocutory order.
You could file the notice of appeal and then file the removal, which insures that the appeal doesn't fail for being untimely if the federal court remands to state court.
But, simply filing the removal before the notice of appeal deadline and then filing a notice of appeal in the removed action should suffice too.
If he initiates the appeal before removing the underlying case, does
the appeal stay in state court?
Probably not. But it's on obscure technical point, so the result may not be 100% predictable.
Does the appeal transfer to the federal courts?
Probably not. You probably need to appeal separately for the appeal to survive the removal, but see above.
The removal process is governed by 28 U.S.C. § 1446 which states in the part pertinent to a federal question removal:
A defendant or defendants desiring to remove any civil action from a
State court shall file in the district court of the United States for
the district and division within which such action is pending a notice
of removal signed pursuant to Rule 11 of the Federal Rules of Civil
Procedure and containing a short and plain statement of the grounds
for removal, together with a copy of all process, pleadings, and
orders served upon such defendant or defendants in such action.
(1)The notice of removal of a civil action or proceeding shall be
filed within 30 days after the receipt by the defendant, through
service or otherwise, of a copy of the initial pleading setting forth
the claim for relief upon which such action or proceeding is based, or
within 30 days after the service of summons upon the defendant if such
initial pleading has then been filed in court and is not required to
be served on the defendant, whichever period is shorter.
(2)(A)When a civil action is removed solely under section 1441(a), all
defendants who have been properly joined and served must join in or
consent to the removal of the action.
(B)Each defendant shall have 30 days after receipt by or service on
that defendant of the initial pleading or summons described in
paragraph (1) to file the notice of removal.
(C)If defendants are served at different times, and a later-served
defendant files a notice of removal, any earlier-served defendant may
consent to the removal even though that earlier-served defendant did
not previously initiate or consent to removal.
(3)Except as provided in subsection (c), if the case stated by the
initial pleading is not removable, a notice of removal may be filed
within thirty days after receipt by the defendant, through service or
otherwise, of a copy of an amended pleading, motion, order or other
paper from which it may first be ascertained that the case is one
which is or has become removable.
. . .
(d)Notice to Adverse Parties and State Court.—
Promptly after the filing of such notice of removal of a civil action
the defendant or defendants shall give written notice thereof to all
adverse parties and shall file a copy of the notice with the clerk of
such State court, which shall effect the removal and the State court
shall proceed no further unless and until the case is remanded.
. . . .
(g) 1 Where the civil action or criminal prosecution that is
removable under section 1442(a) is a proceeding in which a judicial
order for testimony or documents is sought or issued or sought to be
enforced, the 30-day requirement of subsection (b) of this section and
paragraph (1) of section 1455(b) is satisfied if the person or entity
desiring to remove the proceeding files the notice of removal not
later than 30 days after receiving, through service, notice of any