Yes the roads are very dusty.
Imagine what happens;
It's June weather is dry,there is a lot of dust, there
is not much trafic on the roads (most, if not all civil transport is on foot or cart and horse- there are no civil cars, there is no fuel) so, not like on
modern roads with a lot of traffic where most debris or dust is blown to the sides, any dust stays there.
Than the military comes with tracked vehicles passing each other, taking the borders with them, turning to tight/to wide and again there is dust, so it is a good idea to make it look dusty but as I said before the road you intend to make (G.C.220) almost certainly is hard faced.
About the damage; The Wespe weights about 11 ton, the ground pressure is 0.76 KG/CM2 (had to look it up)
an avarage person would do about 0.25 KG/CM2 so, apart from some scratches of the tracks on the surface there is no damage from a single vehicle.
The most damage to roads was done by columns of heavy transport at higher speeds.