Does the app notify you when authentication is attempted? The reason I still use SMS is that I will instantly get notified if someone has my password and attempts to access my account.
Whilst a cunning idea if it catches some unsophisticated crook who just dives in and starts looking for goodies, I'd expect that it's common enough knowledge (e.g. image-bugs dropped in spam to check account liveness) that a serious attacker would either slurp your account via IMAP/POP and browse with external resource loading disabled, or just enable that setting in your gmail account itself, which exists for exactly the reason mentioned above.
The main improvement I can see you've made is that it's real-time enough that you should be able to jump on it straight away and do something rather than the batch processes I suspect spammers use.
There was a cunning|creepy trick used by Facebook I recall reading about not that long ago[1] that relied on Outlook autoloading bgsound attributes despite image loading settings, but I don't know of any comparable holes in gmail.
Since I already get a text message each time I authenticate, I'd even be in favor of one that just texted me each time I authenticated a new computer. That way I could use the security of the app, but the notification of sms.
I believe Facebook used to do just the notification part with some optional security feature where you had to name each new computer you used. They have 2 factor now, of course.
