Yes the yoyos will eat teh snails. But... nothing should be added until it's cycled. Loaches are very sensitive to water quality. Yoyos are very rambunctious and love to play but have never seen them be "tetchy with one another"

Heres some great info on Yoyos-
http://www.loaches.com/species-index/botia-almorhae
With three the tank would be stocked. Heres another loach suggestion and they would take up less room.
http://www.loaches.com/species-index...ia-sidthimunki
Now all that said I really don't like to advise people to buy a particular fish to solve a problem(unless it's a fish they want anyway), better to solve the problem.
Where did the snails come from? What has been put into the tank besides water?
Carol