...ah no per TSA regs Only the passenger should retain the key or combination to the lock.
Make sure you know the rules because mostly they don't.
Just a quick note, that there are really three things you need to be able to comply with:
TSA Regs
Airline "Brand" Rules
Airline Rules
As a guy who is ultimately responsible for ensuring compliance with all of them on my flights, there are cases where my carrier has more restrictive rules on the carriage of firearms and ammunition than the TSA or the Airline "Brand" does. For instance, my carrier used to operate a fleet (of which I was a Captain) that had a maximum quantity of ammunition broken down per "zone" of the aircraft. Which meant that if two guys were seated next to each other that we could be more limited in what they could carry than the TSA regulations did. Of course this came up semi-regularly, because they were often traveling together. There isn't really a good way to check on this in advance, because United/Delta/American are not likely to know the specific restrictions that may effect an airplane flown by one of their subcontractors.
Generally won't be an issue though, but just understand that there are times that you just need to be flexible to make it work. If you are not traveling with ammunition it gets 100 times easier (or at least, there are really only two rules for firearms alone: hard case, passenger ONLY has the key in the cabin).
But we do it on a semi-regular basis. No big deal.
Dan