Yes and no.
That story is complex enough to be worth a movie of its own and it goes back before the Series consoles ship.
ABK was in a bad situation because of mismanagement at various levels one of which was (as revealed in federal court) a...less than cordial...relationship with MS.
When their personnel problems exploded into the public eye, their slide was then greased by Microsoft ("We need to reevalate our relationship with ABK.") and Nintendo (Echoing Microsoft's distancing.) which accelerated the ABK stock price collapse from $100 to $60-ish. and convinced Kotick it was time to cash out.
At that point, ABK did approach MS and others but ABK was and is too big for the kind of deal Kotick needed, a total divestment. All deals were effectively mergers--cash and stock--or partial purchases, which given how ABK was run wasn't viable. (Come COD release time, all studios this side of King got involved.)
Sony, for example wanted COD alone but *which* COD studio(s)? They couldn't afford all of them.
Only MS had the cash, the use for it, and the corporate reputation to both buy ABK outright *and* stem the exodus of developers, deal with the unionization efforts, and stop the stock price cratering while the deal was completed. (Plus the legal staff and political clout to navigate the regulatory hurdles.)
There are plenty of clues that MS was prepared to get ABK long before Kotick came to them, starting with how quickly their notoriously tight-fisted CFO signed off on the massive payout. Basically, ABK was in trouble and MS gave them the last push, knowing they would have no choice but to come to them.
By now, we know that is classic Nadella.
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