Damage to roads is proportional to vehicle weight. The answer is, yes.
The damage to roads by different types of vehicles is pretty well researched and understood.
The damage-to-weight ratio actually scales with the 4th(!) power. Twice as heavy = 2x2x2x2 = 16 times the damage. Four times as heavy = 4x4x4x4 = 256 times the damage. It ramps up very quickly!
One full size truck does as much damage as 100,000 compact cars. Or, put another way, lightweight cars do not cause any appreciable damage.
So yes, expect roads to get literally pounded by all those heavy EVs.