Actually, there's some evidence that increased sleep boosts your metabolism (because your body gets a chance to do all the correct hormonal things it fails to do when your sleep time is inadequate).

I of course consider caffeine an indispensable part of a balanced breakfast... but don't rush to overcompensate. If you can manage even while you consciously feel tired (and surely that's less of a barrier than feeling depressed?), then give your body some additional time to adjust. Sleep is, as you say, not useless.

*hugs*