I am not real sure on this, so take it with a grain of salt. Legally, they would have to sell it to you if you were the higgest bidder. However, there is nothing forcing them to do so (no more than there is anything that forces you to buy it if you are the higgest bidder). I guess it reserves for you the legal right to sue if you win the auction and they don't complete the sale and transfer to you, but it would cost you more $$$$ to do this than it is worth. Most people on the auction sites know this. There is a big difference between LEGAL and what actually takes place. There is a higher probablity of you winning getting LEGAL threats for winning an auction and not completing the transction (since there is money owed) than there is of you winning an auction, not getting the weapon, and suing.
My expeirence is that some people do the 'right thing', others do not.
I have bought off of Gunbroker before and had no problems. Make sure you get a phone number of the dealer/store and call them as soon as the auction ends, especially if you are out of state. Get a name of the person you speak with. Make it personal. Create a relationship. Let them know you are a real person and intend on following through with the deal. Call back from time to time "Did you get the payment?" "Did you get my FFL". You should be OK if you do.
EDITED to add: while I guess you have the 'legal' right to sue, like I said, it doesn't make much sense (unless they take your money and not deliver the weapon). About the most you can do is leave negative feedback (in the case of GunBroker, it is a grading scale A-F just like school. You can leave supporting comments to go with your grade of the seller).