It won't be on your FAA record (unless you're in ST because you failed a QLOE), but it can be on your training record. PRIA covers both, so you need to be more specific about what you mean by PRIA.

For some, PRIA only means that paper from FAA that says they have nothing on file for you.
For some, it means the behemoth of paperwork your previous/current employer sends to your prospective employer. My PRIA response from my previous company was 56 pages.

It's safe to assume your next employer will see that you were put on special tracking.