This situation is used occassionaly in Australia by Medivac flights where they will declare a 'Mercy Flight'.
They are afforded priority - it is usually to do with out of hours crews.
The only requirment is to follow up with a written explanation of the nature of the declaration - but not to the ATC provider, just the Safety regulator.
I could not forsee a commercial operator doing it somehow. It would be bad planning to depart or not divert in the first place I would have thought (the majority of the time).