*** Re-edited after having my first cup of coffee... ***
http://www.groupon.com/faq
It would seem, from the FAQ, there is no immediate interaction between your site and the Groupon customer. With that said, and without having used it myself, here is one possible scenario that might play out...
You enter into a contract with the folks at Groupon to offer a coupon that allows purchasers to buy a $30 item for $1. You are selling this coupon for $5 to Groupon customers if Groupon brings in a minimum of 500 coupon orders within 24 hours. Groupon does its thing and collects its monies, in bulk from its members. Groupon sends you the money and a request for 800 coupons...
I don't think you would get customer information, just a request for an anonymous number of coupons; Groupon's FAQ clearly promises its members that Groupons are transferable...
So you then generate 800 coupons for a particular product ID, that allows the purchase of that product for only $1.
Of course, this is only a half-baked idea, based on the Groupon FAQ. 8)