This is definitely a solution to the registration problem; and metrics will probably back you up on conversion. However, a major drawback of this occurs while moving across multiple devices:

Peter (fictional archetype) might click through on his work computer; then go home, and might want to have another look at the site; however he won't have any recollection of his "personal URL", nor any way to access it. Peter will, at this point, perceive all his time investment going down the drain. He will either re-register (to be wacked on the head when he's back at work again), or refuse the site altogether.

Note this is different in Doodle's case, due to it's inherent sharing nature: people will email the link as part of the main process, so they're able to get back later.

One way to see how this affects user's lifecycle is measuring: 1, username only; 2, username + email; 3, username, email, password variants against eachother, across the entire user funnel: registration, main mechanics, retention (or length of lifecycle).