My guess is "ads on the field" get about as much attention as naming a bowl game for some product, probably less, as the bowl game name gets repeated over and over.
But, it keeps some name of a product somewhat in one's consciousness, and humans are vulnerable to suggestion, sometimes more than logic.
So, next time I'm in "Walmart", I'm going to buy Tostitoes because they sponsor some bowl game? I guess it pays out.
As noted above, if they quit all advertising on "Pepsi" in a few years it would probably be a minor brand, maybe not even that. Now go buy some Tide.
Soap operas.