You need them as long as you have aiptasia. They can find it in places you'll never see it, that is why I like them.
As for getting full...I am sure like any of us, they stop eating when full. The question is, what do they eat when there is no more aiptasia and the answer is, they will starve and die. They will float to the top and try to float away into better waters for more food, not realizing they are in a tank, and there is no where to float to! Try to have a plan to relocate them after they do their job and breed!
How long will it take to clear the bit of aiptasia you have? Just depends how long it takes them to find it and how hungry they are. I have seen them walk right around aiptasia and thought they were doing nothing. I have also watched them eat aiptasia that would swallow a fish! These are the king of aiptasia killers!
Good luck!