It all depends on width and offset of the 18" rim. As well as the amount of drop.
A couple months ago I installed Sparco Assetto Gara 18" that are 7.5" wide with 35mm offset. I'm on coilovers and have maybe a finger gap between the tire and rear fender, and pretty well flush in front. I'm running 205/40/18 tires.
Let's just say that I've had to dremel out the joint between the front bumper and front fender, as well as the rear bumper and rear fender.... just to make clearance otherwise I'd rub. Even now it still rubs in the back on really big dips and if I have someone else in the car with me.
What rims were you thinking of getting??