I would be very interested to hear of any company that did so - anyone?
The reason I would be so interested is that such a subject should be covered in basic AIRMANSHIP.
Furthermore, MAYDAY is a situation in which time is of the essence. I would be very concerned to think that aircrew might be looking through the manual trying to find the right page on which it is dictated by the company whether their current situation is considered by the author (whose decision is, of course, final) to justify calling MAYDAY.
Sorry - IMO it should not be there. Use your basic skills, airmanship and professional judgement. The manual cannot cover all situations. So don't bother covering any. You will merely distract from the immediate problem in hand - flying the aircraft and (hopefully) getting it on the ground safely.