My cat flew collarless by sheer accident -- the morning we were to leave to catch our flight, he knew something was up, and he hid right up inside my couch. The cab was already waiting and I had to literally cut the back of the couch open and pull him out like a C-section birth!! In the process, his collar, an elasticated one, pulled off in my hand. In the frenzy to get him in the crate (he was still highly resistant and the cab was still waiting, plus now we were running late), I never got it back on him again.
Preoccupied with just having his paperwork all present and correct for the animal cargo people, I forgot all about his collarless state when we checked him in at the airport, and in fact they didn't even ask about it. It was only when I was sitting on the plane and I found I'd tucked the collar into my carry-on (it was all such a blur that morning, I didn't even know I'd managed that), that I remembered it had come off!
I was only able to put it back on again at home in our UK destination; so I guess it was of no consequence to the people who handled him at either end of his journey, if that helps at all. This was Continental, and the airports were Houston and Gatwick, but I don't know if other airlines or even airports may feel differently.