Yes, I would expect that the keybind which disables the food and stamina bar would disable the vehicle hud however this is not the reality.
I didn't know that this was a feature in the settings, or I haven't checked in a while, but if they do give a keybind for this they should make the dash lights toggle with a keybind also; or alternatively, give a radial menu when the keybind for headlights is held down, so you can toggle between dash lights on, and headlights on, (the dash is difficult to see in the day time.)
Good post letting immersion seekers know about the vehicle hud setting.