I'm possibly misunderstanding parts of your post, but I seem to sense a contradiction in there somewhere.
On the one hand you mention how Apple and MS aren't necessarily competitors. You therefore conclude that it is reasonable that they work together. I agree.
On the other hand, you also mention how it would be reasonable for Google to offer their services on WP, but the arguments you made for an Apple/MS cooperation don't apply to Google. Google has created products and services in many of the areas where MS earns its money, and offers them free of charge. As a result, there currently is no greater threat to MS than Google, and the opposite is also true. Particularly Bing represents a direct threat to Google's primary revenue streams. That makes Google and MS very strong competitors.
My point is, that I don't think the same rules apply, when it comes to a Google/MS cooperation, as do apply for a Google/Apple or MS/Apple cooperation.
With over 50 million users, MS has already developed a strong enough WP userbase. It already represents fertile ground for Google profits. As a result, I don't think MS having a "strong userbase" is the criteria that counts, because we already have that. What will count is when WP unacceptably weakens Google's userbase. I realize that in a way those are just two sides of the same coin, but I find it's a more accurate way of thinking about it. Unfortunately, its also not really about cooperation.