If you receive a bid you will have the option of accepting it or placing it in auction. You will not accept it or place the bid in the auction if you put it in the other auction.
Let me use an example.. you have a name at Sedo and you place it for auction on Ebay. You do not know it but someone places a bid on your Ebay auction. After coming in from running an errand you log into the net and see " you got mail", you have a bid in Sedo on your domain. Before you click the button to either accept the bid or to send it to the Sedo auction in hopes it goes higher you have to cancel the Ebay auction. Vise a versus. If a bid comes in at Ebay, you take it off the auction at Sedo.
When all this is said there is one more thing to do. If you have any "buy it nows" for your domain names, you had better not have a "buy it now" in another auction, as that is a chance the name will get sold at both places, although like you say the odds are not high.
I don't have buy it now on any domains and I have them for sale at many different auction houses all at the same time. I know if I get bids at both places I can send one to auction and just not accept the other one.
Good Luck with the names selling.