A moment or two of starting to pull it into the garage won't do any more damage. But more than absolutely necessary is bad.
The minimums that should be done are oil change paying particular attention for smell, viscosity and metal fragments. (I doubt there'* metal, but look for it)
Check transmission fluid for smell and visibility. Do not start the car to do this. We don't care about level at the moment. Engine got hot...the transmission is attached and probably got warm as well.
Clearly the car lost coolant...time to find the leak. Easiest way is to start looking at hoses etc. Find a drop and you'll find the hole. Fix problem, fill it up and let it run a while see how it sounds and acts.
So far these motors have only proven to be extremely durable. Let'* see if yours survived as well.
00 Regal GS: All kinds of cool stuff.