I've had a similar feature (without the training part) in GMail for a while now. GMail Labs has a feature called something like "Multi Inbox". It shows other searches/labels of your choice on the front page. I set it up to show Drafts, Starred and a "To Do" label and have been running a system much like this shows, just prioritizing stuff on the fly. Given you can see drafts and such stuff, this might even be a better alternative for some.