The customer may absolutely watch that repair being performed!
However, one thing to keep in mind is that not all repairs are done on the spot. Depending on the severity of a device's damage or type of device, it may be necessary for the iTech to take it to their workshop to complete the process. This is not common but can happen with some iPad repairs or if the device's metal frame is extremely damaged. Just speak with your local iTech about the problems you are experiencing and both the customer and iTech can decide on the appropriate place to have the repair done.