nobody is ever gonna make GSP brawl, making him strike is possible but not brawl that is a mental thing and GSP won't go there.
GSP won't brawl back but I have no doubt that Story could/would barrel forward and push GSP toward the fence swinging his big shots. As we saw last night Story has one hell of a chin, dude actually bit through his mouthguard when Alves hit him with that big knee in the 3rd and it barely phased him... GSP's jabs may deter Story a little bit not the whole fight, Story is determined and would walk right through those jabs to get in close.
Story isn't like Koscheck and Shields etc that let GSP dictate the fight and stood out of their effective range. Story would push forward and make GSP work. That is unless GSP's wrestling is so much better that he could get the fight to the ground at will, something I am not sure he could do cause as we saw Story is a huge strong WW and he has good wrestling ability as well as sweeps and ability to stand back up.
GSP did defeat Alves in impressive fashion but it was also one of GSP's toughest fights imo. Alves was strong enough to get back to his feet and had a punchers chance. I think the Story fight would be similar with GSP having a harder time getting it to the ground and Story being more aggressive on the feet.
I think Story if he fights GSP will be his toughest fight for quite a while. I honestly believe he would be a harder fight then Koscheck, Alves or Fitch were. Styles make fights and if you were going to create someone to beat GSP it would be someone with good wrestling defense and power to finish the fight.