It can be done, but why spray the entire car? I would think re-clearing the offending panel would suffice, and then get the swirls fixed on the rest of the car.
The bad panel would need to be degreased and wet sanded with 800 grit and resprayed with clearcoat, you can't re-clear it without scuffing it first, it won't bond well. Don't worry, even though the scuffed clear will look almost white, when you spray clear urethane over it you'll never know-it will look crystal clear again.
If the part he broke through has a bad edge, it might show as a dip or waver in the paint, so it would need to be feathered without disturbing the base too much, but typically when a buffer burns through it's pretty smooth. You don't want to wetsand the base if you can help it, it can change the tone. If the broken -through area is large, probably best to blend in some base color in that spot before clearing.
Good luck.