If your documents say no later than 2:30, you'll be fine as long as you check in before 2:30. However, I'll second the comment about a cruise not being the same as a flight. A cruise is the destination, not just the transportation. If you show up earlier, you can board, put your things in your cabin, and head to the lido for some lunch. Or explore the ship.
I wouldn't recommend showing up at 10:30 like so many people here like to do. You end up standing in a non-moving line for far longer than is necessary, while you look with envy at those who showed up even earlier and actually got chairs to sit on while they wait...and wait, and wait...
Once they finally do start letting people on board (well before 12:30, I'm sure), the line does move surprisingly quickly, though. If you get there somewhere in the middle, you will probably move right through the check-in process with surprising speed. Like maybe 1:00 or 1:30. If you wait until 2:00, and I'm only guessing here because I haven't witnessed this for myself and haven't seen any firsthand accounts, you may run into a bunch of stragglers and have to stand in more lines.
On the other hand, there are lines in lots of places on board (although none quite that long). It doesn't hurt to prepare yourself in advance and bring your sense of humor! I use them to meet people - kinda like speed-dating, but without the expectations!