Yes you can. The modems have more than one COM port, one for Windows to establish the dial-up connection, and another for diagnostics (which MDMA uses).I don't think you can send USSD codes through MDMA unless you have used MDMA to make the connection. One cannot connect two programs to the same COM port at the same time.
You do not need to have an active internet connection in order to send USSD queries.