Good stuff Marc. Just one caveat; the zero in /mail/u/0 always points to the first Gmail account the user is currently signed in to. If you have multiple accounts, Gmail allows bookmarking and addressing them directly through the /u/0, /u/1, etc pattern (this goes for most Google services like Drive and Maps).
If I’d sign in with my secondary active account, clicking on the Gmail link won’t ever lead me to finding it, not even cleaning up the pre-filled search filter as I’m looking at the wrong account.
Having said that, I bet this will only be a minor percentage of users, so your approach still looks like a cunning awesome way to increase activation time! :)