It underperformed heavily and hit Nintendo financially hard. If the Wii wasn't a success we probably wouldn't have seen Nintendo try to do another console again.
With poor sales figures and the associated financial harm to Nintendo, a Time International article called the GameCube an "unmitigated disaster"
We absolutely would have, Nintendo's console side is not their main area of business. People don't understand just how much money Nintendo makes off of pachinco machines.
Define "console" here. The GameCube was underperforming, but Nintendo was dominating the handheld market with both the Game Boy Advance and the DS. I'm not sure a similarly underperforming Wii would have doomed the company, but I suspect it may have led Nintendo to try a crossover style handheld/set-top hybrid like the Switch a generation early.
Yeah, GBA was a monopoly. They may have given up on the home console business but I don't think their handhelds would've gone anywhere and we probably still would have ended up with the Switch regardless.