First of all no they won't and I think it's sad that even here people are now talking about acquisitions like that, like they are a good thing.
Secondly I hate the "they need X because it would fill a hole in their lineup"-mentality, this idea of feeling the need to cover every base, leads to nothing but mediocrity. Game companies should play to their strengths and think of what they can actually add to certain genres when making games instead of going "Ok, we need a fighting game, a racing game, a FPS, RPG, Jump & Run, Strategy, etc.".
For instance I think it would be great if Sony started exploring JRPG's again, on the one hand because, yes I'm biased towards those, but also because they are one of very few companies out there, that could realistically deliver a AAA JRPG alternative to Square Enix's games as those are not only increasingly rare but can also be pretty hit or miss.
But what could Sony really add to Bungie? I struggle to think of something here.