Inspecting a central AC unit before closing

Don't worry, it's fine.

But if you want to have it checked out, you need to hire an a/c company, obviously.

Try to relax and have a lovely closing.

It's almost certainly fine, but of course the issue with contract representations is there are rarely actual remedies available after closing.

If you want a middle road, here's a simple way to force a little cooling -- turn the system on and blow a hair dryer at the thermostat. If cold air comes out, and you don't hear any horrible noises, it probably works just fine. Plan to have a maintenance company give it a look annually each spring before you start using it.

For bonus points, use the hair dryer to test all the other outlets in the unit during your walkthrough. The brokers may stare but hey...

I don't understand: use the hair dryer to test all the other outlets ~ what/how are you testing? Hmmm . . .

Um, if the apartment is 70 degrees and you set the thermostat to 65 degrees, cold air should come out sans hairdryer.

But yes, it will be impossible to determine if it is functioning optimally if its not 90 degrees out and on for 4 hours. Systems with leaks can still chug away a 10 degree difference and not rear it's ugly head until its really hot out.
As I have a compressor on my roof, Ive been quoted a considerable sum to replace the copper line from roof to condensor.

"Good working order" is vague enough where you won't get to squeeze anything out at closing unless it completely doesnt work at all anyway.

Save yourself the $300 to $500 inspection as you'll end up doing it again in the spring.