I had some experience with snails, yes they do tend to overbreed themselves.
You may have some problems with the rams eating the plants in an aquatic area. I fixed that problem by putting a lot more plants, and the plants that grew extremely fast. Its been working, but every now and then, I have to take the snails out as they tend to reproduce.
I agree it is the common snail, I used it, I like in in my fish tanks, where they are controlled and easily found, but in a vivarium it may become difficult as there will be literally 100's very shortly. So, if you don't mind having 100's of little snails around, I would leave them. If you don't want that many snails, try locating all of them and removing them as quick as possible.
-----
-_^