The Chassis is harder to define in a formula car when you are comparing it to a road car. In all Formula cars the engine and gearbox are stressed members of the chassis. The Monocoque we also call a tub. The carbon tub is the main part of the whole car and can be defined as the chasis.
The rear suspension is mounted to the gearbox in most all formula car designs and to some degree directly to the engine block in F1. Why not add weight to the engine to make it stiffer?? Easy. The goal in F1 is to move as much weight to the front of the tub as possible in recent years.
This puts more pressure on the front tires and allows the car to corner better. The more mechanical grip you have up front means less aero pressure needed. So you have a net gain in speed as a result of less drag.
CFDruss- actually the engine and gearbox are bolted directly to the tub. So whole suspension is dependant on the total torsional rigidity of the tub+engine+gearbox to be effective. The less flex you have from front of the tub to the rear of the gearbox the more effective the suspension will be. It will be more predictable and the engineers will be able to make smaller adjustments to the car to make it handle better.