Id ask lawyers to chime in here but yes. If Brady recants on his testimony and admits guilt and court has already recognizes the appeal hearing as sworn court documents he would essentially be screwed.
Excerpt copied from
this article (more than any layman would probably want to read of arbitration).
Many states’ definitions of perjury include a requirement that the lying occur under oath in an “official proceeding.” Often, the definition of “official proceeding” only extends to “legislative, judicial, administrative or other governmental agency” proceedings. . . . These statutes are ambiguous, at best, as to whether they apply in arbitration. Another handful of states prohibit lying under oath more generally. These states include: . . .
New York . . . .
Arbitration proceedings in New York so
S 210.05 Perjury in the third degree.
A person is guilty of perjury in the third degree when he swears falsely.
Perjury in the third degree is a class A misdemeanor.
S 210.25 Perjury; defense.
In any prosecution for perjury, it is an affirmative defense that the
defendant retracted his false statement in the course of the proceeding in which it was made
before such false statement substantially affected the proceeding and before it became manifest that its falsity was or would be exposed.