Yes, they can charge the surcharge anytime. I don't know what it would do for Public Relations if they waited until the cruise started!
I think they would
just add it to your shipboard account, just like tips are added.
The charges, I think, depend on when and for how long they bought their fuel. If they locked in a price say, until July, then you (and we!) should be okay. If it's only locked in until tomorrow...
. At least I think that's how it works!