I would agree that technically there is no reason you can't interview while on FMLA.

That should not reflect via PRIA/PRD in any way I can think of.

But there is an issue of optics: I would be 100% up front about the situation with the interviewing company (no need to tell your current employer). Some airlines may take the view that since your medical is currently not valid for flight ops, you don't meet their minimums to apply. The computer or HR person who flagged you for an interview would not know that because it just sees the issue date on your 1C which you entered on the application. I'd call or email BEFORE going to the interview.

Don't be surprised if they postpone until after you're cleared to fly.