The precedent is set so it can be done. I know of both RAF and FAA Officers now serving with the AAC and Warrant Officers who have obtained an RAF Commission and fly with them, AAC Warrant Officers who have an AAC Commission and have gone to the RAF, AAC Officers who have gone to the FAA. We even have an AAC Warrant Officer who was Commissioned into the RAF, completed his minimum term and has now just returned to the AAC as an Officer!
I am not certain how it fits with those wanting high rank as it can seriously screw up your Staff College timings and your annual report is bound to question your loyalty but for line pilots, it seems that once you have wings, no one really cares who you fly for.