Are you talking about a strut bar? This does only stiffen the body, reducing flex, making the vehicle more responsive. You can compare it to putting on harder bushings (superflex), or mounting a roll cage. A strut bar can't really affect body roll, since is has no connection to the springs, dampers and wheels.
When driving on a track, changing direction quickly, it is necessary to reduce body roll since you need quick reaction. This might however not increase the maximum corner sped of a GTV, due to understeer that rear wheel passive steering is suppose to reduce when the body is rolling.
Another thing is body pitch when breaking, harder springs could reduce this.