The short answer
Yes — shrimp and snails live together beautifully. Both are peaceful invertebrates that graze algae, biofilm and leftover food, so they make a natural clean-up team with almost no conflict. They share the same calm, cycled conditions, neither preys on the other, and together they keep a tank tidier than either would alone. The only species to think twice about is the assassin snail, which hunts other snails.
Why they get along
Shrimp and snails occupy the same peaceful niche. Neither is aggressive, neither competes seriously for territory, and both simply potter around eating the same surfaces. A colony of cherry shrimp alongside a couple of nerite snails or a mystery snail is one of the most popular, trouble-free combinations in the hobby.
The one snail to watch
The assassin snail is a snail-eating snail — brilliant for controlling pest snails, but by nature a predator. In practice it targets other snails, not shrimp, and adult shrimp are far too quick for it. The only mild risk is to newborn shrimplets. Most keepers run assassins with shrimp without issue, but if you’re breeding shrimp for numbers, keep that small caveat in mind.
Setting up the clean-up team
Give them a gentle filter (do shrimp need a filter), keep the water moderately hard so snails can build shells (why are my snails dying), and feed lightly so a large clean-up crew never runs short of food. Confirm parameters with a test kit, and browse peaceful fish tankmates in good tankmates for shrimp.