Without doubt, the front anti-roll bar increases the stability of the front axle and the rigidity of the chassis. With the roll bar installed the chassis will be more responsive and the roll effect will decrease. This does not mean that an infinitely rigid bar will always improve the set-up: you must always take into account the balance between the front and rear axles. In fact, excessive stability at the front makes it difficult for the driver to manage the directionality of the kart and an imbalance between the front and rear axles, triggering unwanted oversteering or understeering phenomena.
If you mount a front bar, this does not increase the grip of the chassis accordingly, but, if anything, it makes the front end more stable. Having a very stable front is not always a good thing. In fact, a balance must be sought between the two axles to have a balanced set-up. When there is a very stable front, it can be negative for the rear because, for example, by turning the steering wheel to go round a bend, the front will follow the set trajectory while the rear will tend to slide, worsening the kart's smoothness.
Editor's note
The term oversteering basically means a loss of grip at the rear compared to the front. In the article "Setup and driving tricks to reduce oversteering" you will be able to learn more about and understand how to stem this sometimes unwanted behaviour of a kart.