I have personally refused a drink after watching someone pull espresso out of the fridge and dump it in my drink. Espresso is only good for a few minutes after you pull it. After that it starts to loose its intensity and sweetness. It looses all the qualities that you look for in espresso. If you have patrons that understand espresso, once you add that old stuff it just doesn't taste as good.
I would never allow anybody to chill my espresso before serving it to me in a chilled drink. I understand how your employee thinks it helps save time and makes his life easier. But in the coffee world easier doesn't always mean better. I say make him do it right the first time. If your patrons truly understand coffee, they are willing to wait to have it done right!