Well, no. Simply because it will have absolutely no effect on the game whatsoever. If anything, the GAME will drive the story. New modes will be added and be explained through the story, similarly to how TF2 had its Mann vs. Machine mode added. By adding Grey Mann in the comics.
Now, if the question was "Will it be any good?" I'd say that I'm not hopeful, given the cinematics that I've seen and the comics that I've read. It has some good bits here and there but I'm positive that Blizzard won't do anything with them and will just default to having characters that are visually appealing and diverse but narratively uninteresting. If it were me, I'd add in the leader of Talon, that anti-Omnic terrorist group, to the character pool and have him be a charismatic and morally grey figure there to explain that while Talon is a terrorist group that has done some deplorable things, Overwatch has done a bunch of things similar to Talon as well and that the initial motivations behind the forming of said group were much more sympathetic, given that the Omnic Crisis was easily something that most people shouldn't forgive and forget. But I know how this thinly hidden allegory for racism goes, how there's a black and a white side and how good will always prevail and yadda yadda.
Team Fortress 2's comic is actually pretty entertaining and fairly well written as well, and I actually enjoy reading it, unlike the comics from Overwatch, given that they are cliche a lot of the time, battering us with sentiment and attempts at making us feel like a god damn Sandman.