I think it depends on the company. I don’t think most companies would care about the use of a yo-yo. But, I have seen companies that do care when players seem to be representing another brand entirely, not just using their yo-yo sometimes.
For example, let’s pretend that you have a kid who wants to be sponsored, named Bob. Bob is representing one company to death, called Company A. All over his Instagram, Youtube, what he plays, what he wears, what he recommends, all seems to be Company A. Company B might like the kid’s style, and think he seems like a great person, but they know deep down, Bob would rather play for Company A and would fit better with that company. It just seems like his heart is with them.
If Company B sponsors this kid, Bob might just use them as a springboard to inevitably get on Company A’s competition team. That might be okay anyway, because in the meantime, it can be a win/win situation until Bob bails to another company. Or, Company B might be confident enough that they can turn Bob into a fan of the brand, who can represent the company well enough, and stop representing the competition so hard.
I have read a comment from a company owner, that they may have thought to sign a certain player, if he wasn’t representing another brand (not even sponsoring him) to that extent. Personally, I think a company should care what a player likes to throw regularly. If a kid has a case full of a variety of brands of yo-yos, that’s no big deal and not a turnoff. But, if the kid seems to be trying to get the attention of a specific company, and already looks like their sponsored player, it would be a huge turnoff. That’s just my opinion.
So, I wouldn’t think a yo-yo here or there matters, but I think they might be very interested in what you like to play regularly. Why would you want to be sponsored by a company, if you don’t even throw their stuff on a regular basis? :-\