No, not at present, and that's something I couldn't do without hacking the wallet management code itself, or by taking an "outside-the-system" approach like the Bitcoin mixer running on TOR. If the mods proposed at
http://coderrr.wordpress.com/2011/06/30/patching-the-bitcoin-client-to-make-it-more-anonymous/ get included into Bitcoin, though, it should become possible, though still subject to the limitation that someone sending in more coins than the service's pool holds will inevitably get some of their own in return.
Why not create two wallets? Wallet A and Wallet B. When they visit the site it automatically picks the wallet with the smallest balance. They could also select a different one if they are repeat customers so they always deposit into the same wallet every time. They then pick a withdrawal address. As soon as the other wallet gets enough coins it's paid out. They are guaranteed to never get their own coins back. If they are impatient they can cancel it and risk getting paid from the wallet they paid into. As long as you aren't keeping logs it would be impossible to follow as long as you used random pay out times and amounts!