it would help, because users who don't want to be bothered can just create a new account on the fly.

you're already collecting all the information necessary to create an account when somebody completes a purcase, so just make an account for them. include a temporary account password on the email receipt, with a message telling users they can use that pw to log in to the site to check the status of the order. once a week, run a cron to clean up all the accounts of people whose orders have completed and haven't changed the password.

That's better, but I still don't like it because you're forcing a relationship upon the user, regardless of whether or not they want one.