I have a planted Betta tank with about 5 adult Ramshorns and many babies and they don't so much as touch any of the plants (Crypt spiralis, Anacharis, Java Moss, Dwarf Lily, and Anubias nana). If you like the looks of them (I personally do like the little guys) then you can keep them and the population should be okay since you don't feed heavily. I think they are actually supposed to eat decaying plants so they are beneficial. Problems arise when people start with one in a small tank with a fish that they overfeed. Then the snails go bananas.
They MAY do a minimal amount of damage to plants from further readings, but it seems to be rare.