Can I continue downloading Mountain Lion In Sleep Mode? I am downloading OSX Mountain Lion via the App Store however it is taking a while, will it continue downloading in sleep mode?
No, however if you were already running ML, and you had a Flash-storage based Mac that supported PowerNap, then it would likely be able to do so as part of it's ability to automatically download updates etc (which are provided through the Mac App Store) when in sleep.

Bit of a self-fulfilling prophecy though ;)