If I am towing a car, will my odometer reading keep increasing as the car is being towed?

Quick answer - No ! Cars are generally towed with the drive wheels off the ground . If it's a rwd vehicle , that for some reason , has to be towed from the front , they generally would either remove the driveshaft or put wheel dollys to support the rear wheels .If it's a fwd vehicle , that has to be towed from the back , the wheel dollys again would be used to support the front wheels . These days most towing is actually done with a rollback wrecker where the vehicle is winched up onto the flatbed and carried offsite . Hope this answers your question ? I noticed you said " If I tow the car , will ..." . If your car is an automatic and rwd , you'll have to remove the driveshaft before you tow it or the tranny will be damaged . If it's an automatic and fwd , you should not try to tow it yourself or it will damage the tranny . If it's a manual tranny ( fwd or rwd ) you might get by towing it if the tranny is put into neutral but it's risky ! In that case , I think the odometer would be working and probably add miles to its reading . Not sure about that though !

No it wouldn't .
Its explained very precisely by oldblu , so I wouldnt be explaining again !