Oh all right then, I'll do it if no one else will:
If you strike me down I shall become more powerful than you could possibly imagine.
Seriously though it won't force the closure of Bioware proper, just the divison that's making the MMO, add to that that it will probably have a strong start, what with the Bioware fans, MMO fans and Star Wars fans all ready to jump onto it. If it has a strong start, and keeps going for long enough, then either it will gather steam or start dying, but one way or the other it will have looked good for a while.
And also, Bioware have Mass Effect 3 coming out to justify themsleves with, plus that ME2 for the PS3 you see?
If it flopped absolutely they would take a hit, but it wouldn't force closure, and no one would be surprised, because going up against Warcraft at this point is like going up against an angry bear armed with a machine gun. (that's the bear with the machine gun, not you, you have a bottle of tabasco sauce.)