We had friends that did this at port last year in FL and got a great upgrade rate (like a difference of a few hundred dollars going from cat 9 to cat 5)...we looked up what rooms were available on our cruise (first west coast one) and were ready at port w/what room #s to ask for (we had two cat 9 and were hoping to go up to 2 connecting open cat 6)...well, they knew NOTHING at check-in (didn't even know how to check us in for that matter) and told us to ask on the boat....on the boat, they were all confused as well (guest services was less than helpful on several other maters as well, but that's another story) so we ended up staying w/our cat 9 which was fine and definitely livable.
So the moral of my story is...if the gods are smiling down at you, yes, you might have a chance...but if it's overcast and the gods are facing the wrong direction, you are out of luck!