Exactly what "type ride" are you talking about? "If signed off in the logbook" makes all the difference. The training received for the SIC type rating and even a simple "checkout" for a private pilot wanting to rent a 172 while on vacation can be used for an IPC or FR, "if signed off in the logbook."

And, of course, if the training was a check airman for the company and wanted to endorse it as a pilot proficiency check, that would count also.

But I didn't think the OP was asking whether his trainer was allowed to endorse a flight review or a proficiency check for him, but whether the receipt of the SIC rating, without one more word being written anywhere, qualified as passing "a pilot proficiency check conducted by an examiner, an approved pilot check airman, or a U.S. Armed Force, for a pilot certificate, rating, or operating privilege."