There have been petitions that have worked.
Success stories on iPetitions
I'm not sure if this one will, but I do think it would be a good thing of WWE to book Brock for the show.
Against Rusev.
I'm specifically talking about when it comes to wrestling, or perhaps any television show for that matter.
Believe it or not, people actually tried to get a petition going over a decade ago to get HHH removed from the world title picture (this was during his infamous reign of terror from 2002-2005.) Needless to say, it was laughed off. I can also swear there's been a couple of others at some pome point in the past decade, even though none are springing to mind at the moment. There was also a fairly popular character on The Walking Dead that was killed off just last year and a petition was instigated to try and convince the showrunners to bring them back, but alas, it didn't work.
Given Brock is already working squash matches on house shows, there's a fairly decent chance they may have him work the Tribute To The Troops show anyway (although it's largely dependent on if he wants to travel over there into hostile territory), so a petition might prove to be unnecessary.