Complementary upgrades are very infrequent on Disney so I would sincerely suggest you book a cabin that you are going to be happy with instead of hoping for an upgrade which will in all likelyhood leave you disapointed when it does not materialize.
Upgrades happen more often on the wonder than the magic but they still are quite few and far between. Quite a few people say how they are hoping for an upgrade but if you look at it in a dollars and cents viewpoint it would be bad business. If Disney routinely gave upgrades to verandas to people only willing to pay for inside staterooms why would anyone be willing to pay for the verandas? If they encouraged that mindset than everyone would just book the less expensive cabin and wait for an upgrade.
Waiting until after the ship has sailed may give you some bargining room to pay for an upgrade in theroy but I don't know if it would come into play in practice. I would assume all available upgrades would have been paid for prior to sailing. The best advice would be to get to the port early and ask to speak to a manager and see if you could purchase a discounted upgrade. Depending on how full your sailing is that may be a bargin for you but do expect to pay several hundred dollars regardless.
We have sailed on Disney three times in the past two and a half years and have another booked for this December. Not once have we been upgraded (although we book a Cat. 6 from the get go) and I don't expect that it will ever happen. There is no rhyme or reason to upgrades and as I said before it is VERY infrequent. You are best off booking the room you can afford and will enjoy.