If we use deposits on our program registration forms, does the paid registrations enrollment strategy still work?

A deposit does not count as a paid registration because there is still a balance to be paid. So, if you are using the paid registrations enrollment strategy, those individuals will not be automatically enrolled in the class. They will remain on the Registrations tab of the Class Record until you manually flip their status to 'Enrolled' on the Registrations Tab of the Class Record.  This will not be automatic.