Can I hear the phone ringing when the headset is plugged into the PC?

By default, the softphone client sends the ringing signal to all available audio devices on the PC. So if the screen is available as audio output (HDMI, 3.5mm jack connection, USB), it will also ring. There should always be a second audio output (screen, USB loudspeaker, etc.) available in addition to the headset, as otherwise you will only hear the incoming call visually.