"mystery snails" are otherwise known as apple snails. they usually dont come in on your plants, though its possible. apple snails breeding is easily controlled because the lay egg clutches above the water line. its pretty hard to keep them from drying out even if you wanted to have babies.
more likely, it could be what is commonly known in the LFS here as a "trapdoor snail." they are sold as snails for ponds, have browner shells, and the shells are slightly pointy-er. both snails seem to get about the same size (about the size of a golf ball). i have had a few come in on my plants when i pick them up out of the bags they were shipped to the LFS in. they give live birth to 1 or 2 snails at a time and will readily breed, although i do not believe they are hermaphroditic, so if there is just one...no babies. dont quote me on that last bit though.
i can imagine a snail eating a plant if he was really hungry, but a snail being on a plant usually means he is getting something off of the leaves, not eating them. they prefer softer things, like algae and decaying plant matter. i have 3 different species of snails in my tank, including apples and trapdoors, and none are a threat to my plants. however, they also have plenty of green-spot algae to keep them full lol. when a snail eats, it doesnt eat in a circle, but rather a trail that ends up being more like a spiral. they make really cool patterns in the algae whenever there is a thick spot