Banjo is possible. The only requirement is to be a video game character. He's unlikely simply because Rare is owned by Microsoft. It is notable that the Microsoft CEO did say he had no issues with the idea, but it doesn't mean it would happen easily.
Just wanted to clear it up why some characters are unlikely VS impossible. The only impossible characters are those who are severely obscure(Sakurai wants iconic 3rd parties), there's no way the company would okay it, or because they didn't originate in a video game(3rd party rule specifically. It's debatable how much it applies to 1st and 2nd parties, but it probably is a relevant point to look at), also they have to have a video game appearance as is before anything matters.
Anyone who wins the Smash Poll must at least be in a video game, if 3rd party they must originate in a video game, and how likely they are depends on very many factors.
Simply put, Goku is impossible. Brian from Quest 64 is unlikely enough to be impossible due to Imagineer no longer into gaming(whom they have to get permission from), and rather obscure(note that he has a minority popularity at this point at best, but to pretend he's anywhere near iconic is laughable. Banjo is way more known than him, and there's a good reason for that). Note, let's say this character somehow got super high on the Smash Poll. Due to Imagineer's situation, he wouldn't be feasible. He might be someday if the game series gets revived and Imagineer either okays it or gives up the trademark to someone else, and most importantly, does well enough to garner interest. It's an obscure cult classic series with minor popularity.
And yes, I'm using one of my favorite games as an example of why there's more factors than "it's owned by Microsoft". Also, I'd say Master Chief/Jago/Fulgore are more likely than Banjo. The reason is they're more relevant, currently more popular, and their games had a major gaming impact. Halo heavily redefined the FPS genre. Killer Instinct defined combos, created the very well known Combo Breaker, and also is the reason for announcer chatter to be common place.
Banjo is a cool choice, though.
So is Sora(who is pretty darn iconic at this point, more than a lot think. Only thing some people don't know is he's owned by Disney, not Square-Enix).