A good suspension setup and a focused driver will know what is going on. I would take a guess and say the bodies natural gyroscope (the inner ear) paired with peripheral and accute vision are the bodies tools to tell you when things are changing where you cannot see them.
Actually, i wonder what would happen to an f1 drivers driving senses if he were suffering from vertigo, i would guess he would barely be able to feel the feedback through the car and make sense of it.
the 'natural gyroscope' (an accelerometer array) is ALWAYS searching for visual and tactile referencing to update itself
(hence motion sickness and simulator sickness, due to conflicting cues)
even a good reference is only held for 5-6 seconds anyway
(we don't notice this as we are normally updating with non-conflicting (re)referencing)
(any flight school can provide a real-life demonstration of this, the best £100/$100 you could ever spend !)
with visual reference removed anyone can turn and recover a plane by feel if the turn lasts only 5 sec, beyond this everyone's sense of balance is confused by starting to rereference itself to regard the turn as normal ie level
impaired/misleading visual references due to whiteout or incipient ground mist will give problems even on a motorbike
likewise with good visual references if you have a bit of vertigo (which is caused by over-damping of the accelerometers)
........ this all from experience