Yup, that's how it's done. If you don't have a spare box, you can remove your unshot film from the box you have, put it in an opaque bag and in another box or envelope to free up the film box for the lab.

I used to occasionally put film in an opaque bag and an envelope for the lab, if I didn't have a spare box handy, but I've found that this occasionally leads to confusion, so it's safer to give them the film in a film box.