I don't think so. They can do a "Nike, the official sponsor of the Southeastern Conference" but that would only mean they give our HQ $$$$ to advertise. And our refs would wear Nike.
I just don't see how the SEC could MAKE 13 state government funded institutions wear Nike. Now, I could see Slive greasing things and convincing everyone to switch to Nike, but I don't think Auburn would leave UA and I don't think we'd leave Adidas for the same money. It would have to be REALLY worth it.
ETA: A&M is about to become Adidas' banner school. I can't tell you how much Aggie **** I see on a daily basis and I live about as far away from Texas as possible. I'm talking UA-Notre Dame $$$$$$.