The snails won't actually hurt your tank or your fish, and most don't eat healthy plant matter - they will eat dying/dead leaves and algae before chewing healthy leaves (except Aussie blond snails - they will eat your plants to stubs overnight..). Having a few won't harm anything.
I'd only worry if it's very tiny tank, where the bioload become a very big deal and necessitate daily water changes, etc. Huge snails like waterhouse or apple snails have much larger bioloads than a few little pond snails, but the pond snails can quickly build in numbers, so a squishing party might need to happen now and then to keep numbers in check.
My 10 gallon is crawling in snails, of about 4 different species with no harm done at all.
As for 'pet' pond snails - I kept a large coldwater hexagon vase full of them a few years ago. they were fascinating to watch and I very much enjoyed them as pets. Easy to care for (they do need water changes! as much as a fish) and actually quite pretty when they are adults.. They have some very un-snail-like behaviours too, surprised the heck out of me.