It is absolutely impossible for a rate gyro to correct this sort of error.
The calculation used by all popular 3D fusion filters used for consumer grade IMUs assumes that the only acceleration is due to gravity, and that the acceleration vector points vertically. In fact, the accelerometer measurement defines the vertical direction.
Obviously, that is not true in a vehicle that is accelerating horizontally, so you have to measure the horizontal acceleration and subtract it from the observed to get "vertical". It is relatively easy to do that if the accelerometer is fixed to the vehicle frame, but very difficult and very inaccurate if not.