The ground-based radio transmitters used for ILS systems are not very sophisticated and not that difficult to disrupt. (This is why it's not just an onboard thing: taxiing aircraft also hold position some distance from the active runway during ILS operations, so that their radios don't cause interference either). How much disruption, and how much deviation from course, could be caused? Who knows--but do you really want to find out when conditions are down to minimums and the ground is not that far away?!