Can I run the POS on an ordinary Android phone rather than a tablet?

Yes. The same app runs on a phone, and it is the same restaurant management app whatever the screen size. A phone is the natural choice for a waiter, which is why one of the three device kinds is A waiter's phone: it opens on the floor plan rather than the selling screen. A phone can also be paired as A POS that sells if the counter is small. Pair it under Settings → The POS with the six letter code like any other device. The POS and the counter tab in the docs describes the three device kinds.