If it does, I'm 99% sure i'll switch to windows phone. But for that matter, could you also run other PC applications such as Foobar, uTorrent and Samsung Kies 3?
No, not unless Hearthstone releases a Universal app.
Under the hood, these phones are still phones, so traditional Windows executables like StarCraft or Palm Desktop aren't going to run.
Think of it this way, you get access to Windows RT using Continuum with the phones as they are now. The nature of the hardware means x86 appications just won't fly like the original RT.