Just like every animal the peppermint shrimp is hit or miss. You could get one that will take care of it without a problem (if it isn't too big) or it may just ignore them all.
First, I don't like the idea of buying an animal specifically to get rid of a problem (be it alga or whatever). What happens when that specific problem is gone? Many times the animal dies because that is what it eats. Second, you wouldn't want to get anything like that during your cycle anyway because the ammonia could very well kill it.
Getting rid of the aiptasia is pretty easy. It would be even easier right now because you are cycling and you don't have to worry about causing an ammonia spike by killing too many of them because you want ammonia right now!
This tank is packed full of bugs! It looks like I now have a crab, I'm sure I saw a claw nibbling at the rock, I tried to take a picture in the dark but it shot off! I guess these little Gits are bad news too??? Quite cool though!