I can't see why you could not have a window AC unit operating in the house which also had central AC system. I would classify this as an old wive's tale and a possible candidate for myth busters.

I ran a window unit in an upstairs bedroom for over ten years. How would the central air be affected one bit.... except maybe have a lesser whole-house cooling load?

Total BUNK...!

Hey justd your old man just told your mother that crap because she thought one of the rooms was to warm and he didn't want to spring for the price of a little window unit.

Well, if you drop it from the 2nd floor onto the compressor, that might damage it.