If you are saying can I upgrade myself when I get on board then the answer is invariably no as there is so much going on that, to be quite honest, they have either sorted out the upgrades and arrangement of the cabins previously or they can't be bothered with the curfuddle. The chances of being upgraded are better if you are American, they are often upgraded three weeks before sailing, than if you are from the UK but it does happen, if, however, rarely ...... Neil.
If you are upgraded there is no cost to you. All cruise lines bottom up for want of a better expression to try and sail as near to full if possible. To do this long term bookings usually but not always find this out when they arrive to check-in sometimes you know before you leave home but not always, more when you check-in and we have had a few in our time. Does this clarify the point.
One other reason for being chosen and that might be the number of previous cruises with the company, in others like a loyalty option with Celebrity it is Captains club and NCL it is is Latitudes to name two.
I suspect the Independence will be running more or less at capacity this year, certainly over the summer, and the chances of an upgrade will be small. I didn't speak to anyone who mentioned they had been upgraded. They certainly weren't offered at check-in.
You can ask for an upgrade at check in. If there is availability you will pay that day's prevailing rate for the room. The cruiseline may switch your room before you board - especially if you are 2 people in a room that sleeps 4 - so they can sell it to a family of 4 - this would be a complimentary upgrade. This is commonly referred to as a 'visit by the upgrade fairy' - but she hasn't visited me yet!