Should acceleration be included in state vector of a Kalman filter?

Kalman filters are not black magic but the standard way of predicting how a system known only through measurements will behave.

The physics of a car is to a good approximation that of a system of second-order differential equation, except for the source term that comes from the driver's actions and from the slope of the road. The states of the car when the driver is inactive are just position and velocity, the driver's states are the angles of the wheels and the acceleration in wheel direction, the road's state is its slope.

The Kalman filter should probably have the same states, unless these are mostly predictable from the knowledge of the road, and then made part of the dynamical equation rather than independent states. The noise term then just covers the discretization errors of the differential equation for the motion and any change in driver and road states.

On the other hand, in the end only the actual performance counts, and if you have enough data to test the model under realistic conditions, you can simplify the model as long as performance does not degrade.