Is it possible to schedule a makeup into a class that is full?

A makeup can be scheduled into a full class only when the Class Size Makeup Limit (Tools > Edit Settings > Makeup Settings) is set to > 0. 

The Class Makeup Size Limit controls how many 'extra' spots in a class you allow for makeups. If you do not want makeups to exceed the maximum number of students allowed in the class as per the Class Max Size on the Class record, set this to '0'.