Our past experience has been you get told the ship is full but wait until the next day and go and see the purser I have helped get people upgraded before, but there will likely be some charge unless you are lucky, but try if you don't ask you won't get. I even did it on a ferry from Zeebruger to Leith and got us upgraded to a penthouse suite, fantastic but it cost £160 for that one night but we really enjoyed ourselves on the fruit, champers, food and TV, my wife saw the footie match she expected to miss.
You don't say which line your on but the standard answer when anyone requests a change of cabin, for whatever reason, is 'the ship is full & no cabins are available'. Your more likely to get an upgrade onboard if your already in a top end cabin, getting upgraded to even more top end. That said my experiences of Guarantee cabins have been very favourable.......Wilba.