Definitely, I'm just playing with the thought. It rubs my mindset the wrong way saying that God of War Ragnarok would be a first party MS title if they published the PC version.
I've never thought about it on a platform by platform basis, e.g. as soon as MS bought RARE, the Banjo Kazooie games became a MS first party. Whether Nintendo published the N64 games or not have always been irrelevant to me, those are MS games now. But with this definition I guess Banjo Kazooie is still a first party Nintendo game, while simultaneously being a first party MS game.