In an ATC environment with onward coordination I should hope you’re never in the position of being transferred to a unit unaware of you emergency, but a PAN/MAYDAY prefix can be quite handy on frequency for situational awareness or to keep others in check. Without the prefix being used I have been known to add eg “PAN acknowledged” on first contact as much to let everyone else know as to ensure the subject aircraft knows they’re getting the (even more) Rolls-Royce service.