Yes they have potential to produce a relevant platform, end of story ...

If we take the numbers at the end of eight gen with some extrapoloration we could come to the conclusion there aren't lots of Wii U owners compared to either the Xone or PS4, thus making the console not really significant overall. Doesn't mean the console is bad per se. Although the argument could be made that the wii did better with two metroids, zelda's 3d super marios and was more hardcore than the Wii U, but that's a thread for another time. But it does mean it isn't relevant like the Vita which sells like donkeyballs.  

But will they because I don't count either the GC or WII U as relevant, since relevant means competing in therms of sales

then yes, why not? they still have the power and the money to do it.

Yes they very much have a chance of producing a relevant console in terms of sales if we take a look at last gen with the WII ... 

Rumors be damned but I don't like where the NX is headed however before discounting Nintendo I would at least like to know more about it ...

As long as they have money sure they can, Are they actually going to do it? Never unless the company changes big time

Like I said before, if they can make a console that sells in the 30m- 40m range, it should be enough to sell tons of software specially their first party content. Now if you are talking about selling like Wii did, then I will say that it's very unlikely that will ever happen again.

But first we should make clear what "relevant" means?
I think their next console will sell better than Wii U, but it won't be a real competition for PS4 or Xbox One.

I stated in my thread that it means being able to compete with Sony and MS let's say taking an NPD once in a while or at leat being able to sell more than 7.5 million units a year.

Well what if the portable NX sells 60 million units and the console version sells 15 million ... the unified platform thing kinda throws "what's successful" into a bit of a blender.

Which is probably part of the appeal to Nintendo. Now if the console sells like garbage, it doesn't really matter that much because they can still sell the same games to the wider audience that still buys Nintendo handhelds (though that group is shrinking).