I do this with Xbox controllers and it’s very easy. Depending on the emulator you usually have to assign which physical controller should be used for which console input. Usually this is a one time setup unless you switch back and forth a lot between the built in a Steam Deck controller and an external one.

I recommend launching the emulator from Steam when setting that up so there isn’t any confusion between connecting directly to the controllers vs using Steam Input. Once the setup is done you can launch individual ROMs directly from Steam.

You can even mix and match controllers. I’ve played Smash Bros with a mix of Xbox, GCN and PS4 controllers on the Deck.