If the flywheel is horizontal, it will strongly resist roll (where a car's weight moves to the outer wheels on a corner), and may improve handling significantly.
If the flywheel is vertical (very unlikely), the car will resist turning and have very poor handling.
Conservation of angular momentum is the same force that makes bikes easy to balance (slow to fall over) when they're moving.
With a spinning wheel, rotating the axis (axle) towards the plane of the wheel is hard, but rotating around the axis offers no resistance.
More reading.