Can a New Member automatically become a Drupal User with defined Role?
Daniel - have you looked at the CiviMember Roles Sync module which pretty much delivers this as you want. IE when someone joins and has a Drupal user then when they log in Drupal checks their Civi Membership status and gives them a role based on that.

The Rules approach would also work, and is how we are planning on doing this for Drupal 8, funds permitting, but I don't think people have used that approach in D7 since the module gives you the solution out of the box, unless i am missing a nuance in your use case. 

Some documentation about above here