Not at all!
With no mario, no Donkey Kong, No super mario bros, no nes, then no GB and no Zelda and there it goes. Sometime, history depend on a little detail and for video game it was Mario. So basically before saying "oh yes they would still have Wii fit and all" you have to calculate every consequence of what would have happened without Mario which is pretty difficult to do. But it very unlikely that video games would be like we know them today. People tends to fall in a very easy chronological mistake.
Now if the question is would Nintendo survive with no Mario from now on then I will say yes of course. But people her seems to mix present and past with this question.