I'd guess it would be about a $755 repaid. Apple has a tiered rate for repairs, and that's what they charge to replace a logic board.
Don't count on Apple waiving the charge, and certainly don't act like you expect it when you go to the store. Just ask them for a repair estimate and see what they do.
If they quote you $755, consider third party options if you need to save money.
This article in PC World last month has a link to a site that sells replacement screens. For the Air, they start at $139. The next step would be finding someone to install it for you. Look for an Apple authorized technician and see if they would do that for you if you ordered the screen from a third party.
You might also see if your renter's/homeowner's insurance policy (or your parents if you are at home or in a dorm) covers accidental damage. I purchased a rider for my insurance policy that covers accidental damage for $33/year. I did that after spilling a glass on my 2010 (fortunately Apple waived that repair charge, but I figured that won't happen again and $33/year is a lot better than $755).
I wouldn't be surprised to see AppleCare+ expand to other products besides the new iPhone 4S in the future.