It wouldn't matter if you took out two feet of rock and replaced it with soil and geotextile fabric, it will become dry and kill any type of grass you put on there.
During our droughts, turf that is over underground drains will become depleted of moisture and the turf dies. In our case, of bermuda grass, it withers but returns with rains. Other than that, with fescues, etc. it will not recover as quickly.