Nope, they can't even get a grip on the tablet market let alone the potencially dying handheld market...

Short answer: No
Long answer: -

It would fail I think. Japan would never touched and America do not like handhelds. And the nerdy hipsters only buy 3DSs to look cool at conventions anyways. It would appeal to no one nowhere.

Nah, they would need creative studios to make games that would sell systems. And Microsoft first parties for the most part is non-existent except for the main stream stuff like Gears and Forza which is bland as fuck.

It would fail and I doubt it would do better than the Vita simply because the Vita at least has a stable market in Japan. I don't think the same can be said for a Microsoft handheld.

Why?  How?

In the west, older demographics have moved on from handhelds.  The only way to secure customers in western markets is with games that appeal to kids.  Nintendo has that while Sony completely failed to grasp that fact.  Microsoft has even less appeal IP that would appeal to kids than Sony.  They would literally have to start from scratch and hope they found something that became a big hit.

In Japan?  Yeah.

it would fail. What kind of games would MS put on that? Halo and gear are made to be played on the big screen with multiplayer.
They would need games like Pokemon, Mario Kart, AC. Those are games that you play in short bursts, which is the whole idea of owning a handheld.

Probably not... Thinking about it, what Microsoft product is popular now day?

i may be wrong but it kind of seem like:

Win8 was kind of a flop
Windows phone don t seem to take over
Surface is cool but who buy it? (Beside me...:S)
And the xbox brand is kind in a bad shape right now.

I blame don mattrick ;)

I made a thread about this a month ago.

eh, it would do ok.