If you were to ask me today to design a new chassis I would likely start with a chassis torsional stiffness that would be high enough that you would neglect it in the suspension design. As you can imagine there are enough variables to deal with that eliminating one makes the job somewhat easier. That is what conventional Race Car Design theory would recommend.
Honestly I don't have an answer as to how much effect changing the chassis torsional stiffness has on handling. As a guess I would expect the torsional stiffness of the chassis to be 10 times that of the suspension. That would mean 90% of the handling is suspension and 10% is chassis. If you can change the chassis stiffness by say 10% then that would have a 1% effect on the overall chassis + suspension stiffness. Not huge but possibly significant. Keep in mind I'm just guessing here.
My personal opinion is you don't want to use a uncontrolled spring to adjust the handling of your car. That is essentially what the torsional stiffness of a chassis is, a spring. If you don't have a damper (shock) to control it you risk going unstable if the chassis stiffness is close to the suspension roll stiffness. I prefer to use known quantities like springs, shocks, ARB's and roll centres to adjust the handling.