It's not likely. I mean, not just that such a thing would never happen on straight legal grounds, but also because Peter Parker would simply whup him silly.
Admittedly, this isn't a legitimately sanctioned bout, because the legal complexities between Disney and Warner Brothers would take a whole army of lawyers to unravel. It's also nowhere near as gruesome as yesterday's UFC bout between Anderson Silva/Chris Weidman, if you watched that.
My inner comics nerd wants to shout that, even banning web shooters or utility belts, it's still a horribly mismatched bout, though. I mean, Peter Parker has the proportionate strength of a spider, scaled up, which means he's logically hundreds of times stronger than Bruce Wayne. Even with help from Dick Grayson, he's still going down.