We have an single "on call phone" that we pass around. Can On Call Central still work with that?

Yes, On Call Central can work with that. However, we discourage this sort of setup due to the following reasons:

• Many of the reasons for using an "on call phone" just don't apply when you use On Call Central. For example, many practices don't want to have their personal caller ID shown to patients. On Call Central prevents this from happening anyway. 
• On Call Central is engineered with the notion that there typically is a 1:1 relationship between a device and an individual. We use the caller ID of a device to determine who is calling into On Call Central. When a device is shared by multiple people, this assumption is not valid, and you can get some odd results.
• Part of the benefit of On Call Central is that it produces a very clear trail of all messages, notifications, and responses, and is able to link each event back to an individual. Sharing a device prevents us from being being able to tell "person X heard this message at a certain time."
• Sharing devices will make it difficult or impossible to troubleshoot several types of common issues. 
• Sharing a device in order to simply reduce the number of On Call Central user seats explicitly is against our Terms of Service. If you choose to pass around an on call phone, it will not reduce your service charge.