Binance goal to become a sponsor certainly cannot be separated from their goal to promote binance to be bigger, I think the impact on the promotion will probably have an impact on BNB, although not too significant, because after all Binance goal is not only to form a partnership to promote increasingly making them famous, but behind that they also want BNB to be able to grow, increase or decrease in the price of bnb be influenced by the volume of transactions that occur in the market, but with this collaboration I think it will affect many people to find out what it is real binance, so that in the end people will know firsthand the relationship between binance with BNB, and in the end people will try to buy bnb in the market thereby increasing the volume of demand in the market.
I am not so sure that exchange sponsorship should be that much impactful when it is this little. Look at crypto.com, they have sponsorships all around the world, Lakers, F1, premier league, they have so many places that they have sponsored right now and it didn't work to make them bigger than Binance.
It did however helped them grow bigger, if we are comparing it to just how big they were and how bigger they are right now then it worked perfectly, but not bigger than binance. This shows the power of sponsorships, it means it can't make a place "that" big, it makes it big, but Binance is already at the top so I do not know how much they need it.