No, the shock (we don't have struts) towers don't do much to stiffen up the overall structure of the car. The sheetmetal isn't that thick though and can flex a bit which causes deflection of the suspension. Sticking a bar on helps get rid of the deflection.

Of course most people won't be able to notice the difference and are just convincing themselves that something about the car is different...but it does have a functional purpose.