So just to confirm, Mt.Gox only needs ID for withdrawing. If you are autotrading you don't need ID until you come to withdraw:
and you can get around that by withdrawing <200BTC/day.
Until the day that they disable withdrawals and insist that you verify your identify. That has happened to numerous individuals, regardless of the amount they are withdrawing. The terms of service when signing up assert that they can require identity at any time for any reason, and hold your funds until you do so.
So is ID needed for deposits too? My worry is that this should work but then all of a sudden we get a request for ID anyway.
For Dwolla deposits to be credited, verified identity is required. There appears to be more leeway for deposits of other methods (e.g., redeem voucher code, BTC deposits, etc.)