you should auto-gen an email address for every new visitor, makes it easier than having to check. people don't care what the username is for a throw-away email address anyway.
after auto-gen, set a cookie so if I do have to come back for something, I don't need to remember the username and I can click a link to see the inbox (or just put the inbox on the frontpage as well)
otherwise, pretty cool! a neat hack would be a bookmarklet that auto fills-in a reg form with the email address (say some javascript that searches for an 'email' text field and inserts a new unique email).
edit: come to think of it, I would probably pay money if you did this as a service for my own domain. eg. I could point a catch-all for all my email to you, which you can use to generate throw-away emails from my domain name (in that case the emails are less likely to be blocked by services).