Really? My guess is that, if that is true, Sony won't choose AMSD for PS5.

Because of what? Sony and MS do business all the time. If they'll get the best offer from AMD they will choose AMD, regardless of wether MS owns them or not. If MS buys AMD, it'll be a division that is entirely separate from the XBOX division. For example, the PS4 uses some DRM software developped (and licenced) by Microsoft, the XBO uses blu-ray even though Sony is part of the blu-ray consortium and thus makes miney on every blu-ray disc sold.

Is AMD profitable? $1.8bn isn't much for MS and even if they don't buy it, MS was probably already planning to stop making consoles at the end of this gen.

Well, Sony tries every gen to make people think their Playstation is the most powerful system and they do that quite successfully. With PS4 they made several adjustments to a vanilla AMD design MS obviously didn't know about. If MS buys AMD now they know exactly what Sony is planning and can build an even better system. Or can sell Sony tech they already improved to make use of it alone.

 Their technology is valuable. Imagine the horror on Intel's face if MS would buy AMD, even though I think this is unlikely.

Hm, that's a point I didn't consider. Oh well, I doubt this is true regardless, but it would be a rather interesting scenario to watch unfold! xD

Keep in mind Nintendo aren't even showing off what the NX might be in terms of home system or handheld... even an Operating system so that their competitors can't get a head start on developing a product to rival it, it would be very unlikely for Sony to ask Microsoft to develope portions of a console for them and think that MS wouldn't use the information to 1-up their hardware.

Surely MS doesn't want to compete with Intel, their unofficial vertical duopolistic cartel in PC market is of the essence for both. Sure, MS can benefit from Intel having some competition, but Intel too doesn't want to become formally a monopolist as it would be targeted by antitrust, so while both need AMD alive, but possibly depending on their benevolence (for example AMD can't avoid accepting cross-licensing deals very one-sided in Intel's favour), for the interests of both MS is the least suitable investor that should save AMD.
Both for tech and wealth and power, and for user's sake too, the best saviour for AMD would be IBM, but neither Intel nor MS would like this very much, for MS it would be acceptable on consoles, but dangerous on PC, smartphones and tablets, for Intel, if IBM were really focused to make AMD powerful, it would be a nightmare in every market, those that it already dominates and those where it'd like to expand.

Super smart idea, would wipe out PS5. If PS5 would be a traditional console anyway.

They better do as PSNow is not a substitution for the gaming we know.