They'd survive and do decent-to-well, but it would never be the same and the industry would be changed in general for the worse IMO.

Yes, they could survive. And they'd thrive. The future would be better if they stayed first-party, though. I like that Nintendo is the only first party that tries to set its consoles apart from the competition in a considerable way, even if it sometimes results in the lack of competitiveness to begin with. This is something that I hope they can fix with the NX, but we'll see.

If they did then I'd wager that Nintendo would be even moreso adverse to risk than they are now. For example, we wouldn't even be getting games like SF0 or Splatoon. Also add on the idea that they wouldn't be working on their own hardware anymore and I can see a noticeable decline in their game quality.

In the end if such a thing came to pass then the industry would be a worse off place. It would also even edge me toward the idea of not wanting to continue playing video game period.

EDIT: To answer the question more clearly, yeah probably. But who knows for how long. 

I believe they would thrive as a third party studio. However, that is not happening anytime soon and probably never.

Yeah, they would. However, a lot of the aspects of them would have to be watered down/disappear completely. They'd have masters to answer to. And would have to fall in line, on the things they put their stuff on. They'd also have to downscale a lot of aspects. Like their stores. I wouldn't be surprised they would get closed, at some point.

They would do good if that ever happens.

I keep wondering that too. IMO Nintendo's wacky controllers are exactly what have kept Mario and Zelda fun and interesting over all these years (because it sure as hell hasn't been graphics or story.) You take that away and put these franchises on PlayStation with only a standard PlayStation controller to work with... I mean sure, the first few games would be great, but I just can't help but feel they'd get stale after a while.

They'd survive but would likely decline steadily.

Can't really say, depends on if they still want to make crap like garbage festival and color trash, but assuming they don't and assuming they support both Xbox and Playstation, then yes as they'll always have a solid installbase to sell to and their games would greatly help sell those systems. With that NX controller they've got, I'm seriously starting to think we'd be better off with Nintendo going 3rd party.

they would survive, but it would not be the same Nintendo we all know and love today.