In the Mix IDE is it possible to view the tokens a user currently has in their account for debugging purposes.
Tokens are not really stored in an "account". A token is just a contract that meets the API requirements set out by EIP 20. Since the user's balance is stored in the contract and not in the user's account, you need to know the address of a token contract in order to check a balance.
Thus, if you add the token contracts to Mist, it will automatically display a user's balance, but it is generally not possible to enumerate all tokens which a user owns.