No, you don't get anything really. Not even a good story sequence. He literally gets out of bed, says he's feeling better, tells you he built a raft and sends you on your way. He then stays on the island for the rest of the game and simply mumbles something about you finding your friends and hope and all that nonsense. It is more emotionally fulfilling to let him die, cause Celes' suicide attempt is just a really poignant moment in the game for most.

There will be a reason to come back to the island later, just to pick something up, but Cid's survival has nothing to do with it, so you're good. You've now reached the point in the game where things will get harder, and it's really easy to get lost in doing everything. It may be difficult to not spoil certain things at this point, but feel free to ask questions. Just be sure to talk to all the NPCs. they will point you in the right direction, so you don't have to ask us. It is very easy to miss some stuff in this part of the game.