Bad idea.

Well, I suppose the more logical choice would be to co-operate with Sony (PS4) in Japan if so. The PS4 owners I assume would be more interested in the X1 exclusives that they have than the Nintendo owners, I believe. Still, FPS and shooters are not really Japanese target games, so they would most likely not do too well even on the PS4.

But also this could not work for many reasons, and one of the biggest is export of games. If someone in Europe or North America could import Halo 5 for their PS4 it would just damage X1 in those regions. And of course the same way for Wii U owners, if they could import the games, it would surely damage X1 as well.

One partnership however that I think could actually work, if MS has no plans to enter the handheld market themselves is if they partened up with Sony to release some new handheld device and/or just their 1st party games. To be fair, the Nintendo-consoles has total domination of the handheld market so a partnership between Sony/MS on this would perhaps benefit the market some, as well as both companies. But if they want some more guarantee of money they should of course partner up with Nintendo (3DS) and/or release their games for Windows Phone. Or even go "mobile-multiplat" and realease for Android and iOS as well.

But the idea you wrote of, I don't believe it's a good idea at all. But yes, probably better than their current situation if I pretend that their games would be JP-locked and could not ever be played on a EU/NA-console.

Thats bad idea for MS, if they really wanna penetrate the japanese market they should make a joint venture if sega there