Most jet engines will fail quickly if exposed to that Iceland dust.
Why?
Because the engines' first stage turbine blades run in gas temperatures above their melting point. They don't melt normally because cooling air is blown through a multitude of small holes in the blades. If the unfiltered cooling air contains the Iceland dust this will rapidly clog up the cooling holes.
Result is melted turbine blades which break away to destroy the turbine causing the hapless pilot of the instant glider to pray while he transmit a May Day.
Piston engines will probably be OK for a while until their air filters choke off the induction air flow. Same with your cars.