Can you use Duolingo Schools to assign TinyCards practice decks?
No, sadly not. There's also no way of assigning strengthening a skill, or assigning a homework of golding the tree, or keeping it gold, or earning XP that isn't from endlessly repeating the first lesson of the first skill, etc. There's also a lot of detail about your students use of Duolingo that you won't be able to see.
It's also not possible to share a classroom between teachers, or hand a class over to another teacher, or to import users by uploading a CSV file, etc etc.
It's still relatively early days for the Duolingo for Schools system, and there's a lot of stuff that a teacher needs that hasn't been implemented yet. ...though I admit I'm surprised we're still waiting for all of that stuff.