That would be an expensive gamble. If say I bid $5000 on someones kite who's to say that Kent (we know he'll bid high) doesn't bid $5001 on a different kite. Then Kent gets that kite and I am still out $5000 for the kite I bid on.
Yes, as long as there were two crazy people out there willing to give up what they bid, the contest should be fine. If the bids were published then someone could just wait for a few minutes before the cut off to bid. Again, as long as someone else was willing to keep others in check by also bidding a crazy amount, everything would be fine.
My recommendation would be to keep bids private. This would also stop someone from out bidding the last person by $1.00. Hiding the amount of the bid means that the person willing to pay the highest, honest amount, wins (not the highest by $1).
I'm certainly not promoting it and I'd hope everything works out fine. I certainly don't have skin in this game so it's just my 2 cents.