I don't think so.
Mario, Pokemon and Zelda, their major franchises, would only get even more famous.
Their minor franchises are not competitor to AAA games, they are still their own thing (except some few like Metroid), but Nintendo will always be Nintendo, their brand power is enough to put them on evidence, and like Square Enix or Ubisoft for example, even their simpler games will always have their audience, and free marketing will grow a lot just as well.
just pointing out the obvious, but the Mario spin offs (Smash, Mario Kart, and even Mario Party at times) sell competitively with big AAA titles. Very few triple A games end up selling at the level of like an Uncharted or Call of Duty.
also Metroid, Animal Crossing, Pikmin- all sell millions of copies. Hell random things like Splatoon and Mario Maker sell millions of copies. I also think if Nintendo would focus on some of their dormant franchises they would kill it with them too (Advance Wars, remake Wave Race, do a contemporary Earthbound, etc.)
you are unaware of what ends up happening to third party developers. They lose a LOT of control in terms of some decisions (release dates, some levels of design (have to be forced to mesh with the hardware). Also they share profits with the hardware manufacturer.
People tend to forget Nintendo makes a lot of money by selling accessories and generally also makes money from the hardware sales themselves (if anything the Switch accessory prices will serve as a reminder of that).
Going third party at this point does not benefit Nintendo. if miraculously the Switch is abysmal failure (I find it hard to imagine, but still) THEN maybeeee talk like that will be justified as an option. I still would doubt it, when you have franchises like Mario and Pokemon its like printing money so I just don't think Nintendo will ever really be in a dangerous enough situation financially to feel the need to do something that drastic
however I could see exclusive DEALS, like a Microsoft paying Nintendo to put one of their titles on the Xbox or something.
ironically anyway I think the Switch as far as hardware looks GOOD, its the software announcements that are lacking at the moment. My point being that its not even as if Nintendo seems to currently have a lot of games immediately coming, being third party at the moment for example would be useless.
NES classic sales and 3DS continual sales this holiday (both selling out a lot of places) are reminders that Nintendo's IPs are too important to not make their own hardware IMO. If anything maybe they could use a push in the right direction in terms of broader system decisions though, I wouldn't mind them partnering with a big tech company to design some awesome piece of gaming hardware in the future as some form of hardware. But they definitely need to maintain some control over the hardware either way. Nintendo's best results tend to come from being free in terms of creativity and the hardware and software dynamic. Although I will admit feeling slightly concerning about the sort of return of motion wii motes with these Joycons, ugh :/