Yes, Assasin snails will breed in your tank. The babies will have slightly lighter yellow stripes on their shells.
The Assasins bury from time to time, not all the time. They can stay hidden like that for weeks on end. Chances are if you have seen one baby you have more.
Always remember that Assasins could be hiding in your gravel and don't add nice snails like Neritinas or Tylomelanias to that tank. I saw this Orange Tylomelania being sold in a German website for 30 Euros (about 45 USD). You don't want to put him in a tank where you could have Assasins hiding
--Nikolay