I have a functioning rotary phone connected to POTS. I do live in the sticks though. Only issue is automated systems that ask me to dial 1 for foo, 2 for bar, etc. But a lot of those now actually also take voice.
No, the dialing on a rotary phone is done by quickly closing and opening the circuit (this means you can tap out numbers by hand on the switch that detects you hanging up the handset).
Press 1 to continue systems require the DTMF tones to be played down the line, either by the phone or any other device held up to it.