... perhaps there was more chance that they would already have the necessary floatation devices in their inventory and experience of using them in mid-ocean and rough seas. Did the RAF posess these floatation devices themselves? Were they specially developed for Operation Corporate or were they already in the inventory prior to Corporate? Or did the USA supply them?
Nimrods, Shackletons before them (and very likely Neptunes and Liberators before
them) have been dropping supplies to the Navy for donkeys years, day and night and in all kinds of weather. Little difference really in dropping from the bomb bay of a Nimrod or kicking it off the ramp of a Herc. Occasionally the flotation devices fail - such is life.
As others have said, other than regular MAC provisioning flights into ASI, there was no USAF air activity from there during Op Corporate. Lots of support was provided in many different ways, but Americans flying from ASI in direct support to a UK operation? It didn't happen.
But that's not to say they won't make a movie about it.