I would love to see a partnership like that. Switch basically becoming Microsoft's handheld, and Xbox basically becoming Nintendo's home console. If Google does release a next-gen console like some rumors suggest they will, Google could be very steep competition next-gen since they have alot of money to throw around and moneyhat studios and exclusives with. Such a partnership between Nintendo and Microsoft could be their best chance of surviving in a 4 console market.
I mean it would be insanely powerful, and I don't just mean specs wise. Imagine if the next Switch docked in the next Xbox? Or hell, what if the Switch Pro does? Could solve Nintendo's weird problem with having a console that's sort of in between gens and is just getting momentum when the next generation starts. They release a Switch Pro that interacts directly with a next gen console and people have an all new reason to buy a Switch while long time Switch owners continue to get games developed for the Switch and Nintendo doesn't have to release a new console and cut the Switch's life short. Brand wise it fixes Nintendo's kiddie image while bolstering Xbox's family friendly image. That said I don't see any cross branding happening, aka no "Xtendos" or "Nintendoboxes" at least in official branding, Nintendo Switch and Xbox would keep their separate brands, just happen to work together.
As for a Google console, I don't think it would last. The video game console market isn't really quite big enough for 3 companies as it is. Nintendo has survived by finding a niche, be it motion controls (until they were everywhere even as the fad was passing), portables (until smart phones slowly suffocated that market), and now hybrid consoles (which seems super promising, but only until other companies develop their own version, which this partnership would save Microsoft the trouble of and Nintendo the need to find a new niche). Google would have tons of money, but unlike Microsoft, who came into the gaming scene with no reputation for console games, only (often very good) PC games (and Bill Gates, nerd legend, that definitely helped), Google would come in with a reputation of not having actually developed any games, just owning a smartphone app market full of shitty games. It'll be like Ouya but with bettering marketing and more money. Whether Microsoft and Nintendo teamed up or not, but especially if they did team up, Google would be out after one or two gens.
Even if Google doesn't enter, it might be something Nintendo has to do eventually, and certainly fits in with the direction Nadella seems to be taking the company. So I could believe this rumor if only because it would work so well. That said it's way to early to tell with a rumor this huge. Still, it's fascinating to see how quickly this thread blew up. And not just with "yeah right" posts, but with people genuinely discussing the possibility. It's a very intriguing one.