Have visited the tower whilst a student at the college next door. I can't remember if they have an ATM (small radar in VCR used for informational purposes) but am pretty certain they did. However, downstairs they also had a normal approach radar facility which is where you would have been given your squawk on entering the zone.
To answer your original question, the controller would have still been able to keep you all orbiting with a picture in his head using his flight strips as a guide.