Yes, it sounds like a list would be needed in this case.
You could have a SharePoint List with each item being the individual appointments:
- Tuesday 8am
- Tuesday 9am
- Thursday 8am
- Thursday 9am
In order to submit data from a regular InfoPath form (not a list form) into both a Form Library and a List, here's one method: http://www.infopathdev.com/blogs/matt/archive/2006/02/02/Add-SharePoint-List-Items-with-InfoPath.aspx (there may be other methods - quick Google search will find those).
qRules also includes a command (SubmitToSharePointList) which performs this action. You could use qRules to map data to that list from your form library form, and label each appointment as "Busy" and even add who is booked for that appointment.
http://www.infopathdev.com/blogs/hilary/archive/2012/05/30/qrules-submittosharepointlist-walkthrough-for-v4-2.aspx
Hope this helps!