The auction house would be foolish not to be data mining everyone's bidding history.
And absolutely they record the underbidder, for the reason floortrader mentioned. When the underbidder was a live floor bidder, I've often heard the auctioneer say, for his record keeping, "and the underbidder was bidder number 67" for example. Especially when a book bidder wins at his top limit, they need documentation to know there were actually other real bidders that ran the book bidder up to his limit.
Never at a public auction have I received thanks for being the underbidder, but it has happened on
ebay more than once.
Maybe there is too much liability involved, if a token gift or even a Thank You email were presented to the jury, it might look like the auction house is colluding with a shill bidder.