Yes they will still work but you will be traveling at the same speed as the light being emitted from them so there will be no time for the light to go forward hit something and be reflected back to your eyes.
Light is not actually a particle so it is not affected by the momentum of the vehicle. As far as the light is concerned the headlight is stationary at the time that the photon is emitted.
If it were a particle, the parabolic mirror used to reflect the beam forward would create some interesting effects as some light would be traveling backwards at the speed of light and the headlight would be traveling forward at the speed of light with all sorts of collision implications.
