Kohanim as doctors

I understand that halacha is pretty clear in prohibiting Kohanim from becoming doctors due to concerns about coming into contact with a corpse.

However, what if a Kohen is already a doctor, around dead bodies, and plans to continue practicing? Would they hypothetically immerse in a mikveh before performing their priestly duties? Would they be disqualified from participating entirely? Does pikuach nefesh override this prohibition if they already underwent the training to save lives?

Or is this truly a moot point in that no observant Kohen would ever be caught in this situation (and thus halacha has little to say other than “don’t be in this situation in the first place”)?