I've never tried it, but I would not recommend counting on it.
On almost every cruise we've taken in the last several years, the ships have been fully booked. Most have had a little sign sitting on the purser's desk saying they are fully booked. Which is obviously there, to stop people from wasting time in line, asking about upgrades. And even if there are better cabins available, you will have to pay for it. And that price is not necessarily any less than it would be today. More likely it'll cost more.
So if you really want a better cabin than you have, remember this: One of the most commonly offered bits of advice that you'll see here on Cruise Addict's is this: Never ever book any cabin catagory less than you will be happy in, because that is most likely the cabin you will get.