Is there a way to have ringing come through the general speakers and the phone call through the headset?

Unfortunately, we do not control the way the operating systems control audio devices. We can only play audio on the Google Chrome default device.

To ensure that your agents are notified when there is an incoming call, even if they are not wearing the headset, you can enable Desktop Notifications. Desktop Notifications allow your agents to see a screen pop as the phone rings, even if the browser is minimized.