Not sure about assassin snails although I'd assume so. They will definitely eat ramshorn and pond snail. MTS they tend to not go crazy over. They'll eat them, but since the snails are hard to eat and spend time in the substrate, they're usually not totally eradicated.
This is all generally true of all the loach species from the genuses Yasuhikotakia and Botia.
They leave my Nerites alone, either dont touch or barely make a dent in the thosands of malaysian livebearing snails, but ramshorn and other common forms have been reduced considerably.