I tried to move a deposit for an NCL cruise before and my TA said he couldn't do it. I'm not sure if he really couldn't or didn't want to. The original cruise was booked with a different TA at the same company. No idea if that would affect his commission somehow.
I feel like there's no harm in trying it though, other than floating your money. It's not a definite that Amex will claw back if it's way down the line, though you should assume they will and just be happily surprised if they never do.
In general, booking through a
travel agency the payment will still be directly with Celebrity. Exception would be some sort of group rate where the agency has fronted some money, then some/part of the payment would be to them. Ran into this once unexpectedly.
If you have an Amex Platinum card, you can get extra OBC with the Cruise Privileges Program. You do not have to go through Amex Travel to use it,
just need to find a participating TA.