Can the auctioneer bid at an auction?

Yes. The rule is that the bidder is making an offer to buy and the auctioneer accepts this in whatever manner is customary, usually the fall of the hammer. A bidder may withdraw his or her bid at any time before the fall of the hammer, but any bid in any event lapses as an offer on the making of a higher bid, so that if a higher bid is made, then withdrawn before the fall of the hammer, the auctioneer cannot then purport to accept the previous highest bid. If an auction is without reserve then whilst there is no contract of sale between the owner of the goods and the highest bidder (because the placing of goods in the auction is an invitation to treat) there is a collateral contract between the auctioneer and the highest bidder that the auction will be held without reserve (i.e., that the highest bid, however low, will be accepted).