Simply, no.
Why would Blizz ask MLG for money when they have plenty $$$ themselves, and when they see that the success of professional starcraft (in the West, at least) depends upon organizations like MLG? I'd be very suprised if Blizz takes money from MLG.
Blizz is very aware that SC2 is struggling a little bit, especially when it comes to the casual player base. A healthy pro-scene needs a sizeable player base, and SC2 is lacking in that regard. That's also why Blizz announced some new features in the upcoming expansion, having to do with tournaments for casual players, etc. (
link)
Blizz full well realizes that this is a make-or-break moment when it comes to Starcraft as an eSport in the west, so if anything, it'd make sense for them to financially support MLG instead of taking money from MLG.