I wouldn't call those ties very deep, Sega still releases more exclusives for Sony than Microsoft. The main reason the Sega/Microsoft relationship happened at all back in the 6th generation was because Microsoft was trying so hard to break into the Japanese market with their brand new excursion into the console business. Microsoft was courting every Japanese publisher who would give them the time of day. But Japan is fairly xenophobic when it comes to the products it buys—obviously there are major exceptions, but despite Microsoft's best efforts during the 6th and 7th generation, and many Japanese publishers getting on board, the Japanese public just never gave any Xbox the time of day, they literally sold worse than the Vita there—maybe even the Wii U. They seem to have largely given up during the 8th generation, and while I could see them making another attempt, they've got virtually no market share whatever over there, and buying Sega wouldn't be enough to change that.
As I've attempted to explain so far in my last couple posts, the Japanese audience would respond by ignoring the fact that Microsoft has a gaming console, the exact same way they've done every time Microsoft has tried to establish the Xbox brand in Japan. There were some fairly highly regarded Japanese-developed Xbox-exclusives in the 6th and 7th generations, and Xboxes still sold like crap in Japan. One medium-sized Japanese publisher that's been pretty inconsistent in delivering quality titles over most of its existence isn't going to change that. Even if Atlus was included in the deal (I'm pretty sure they're owned by SEGA's parent company, not SEGA themselves), it still wouldn't make a difference, and if Microsoft has learned anything from its previous experiences in Japan, they wouldn't even try to enforce any kind of exclusivity on any SEGA or Atlus titles in Japan, they wouldn't make any money.