They shouldn't, I have 18" rims on my RSX as well and an aftermarket body kit which decreased my space even more than it was previously. I have no rubbing issues whatsoever so I think you should be fine. And another thing is that even if you do notice they rub a little bit, just raise it up a tad (this is assuming you are getting adjustable coilovers) It depends on what kind you're getting and how much of a drop as well, check out www.clubrsx.com in the suspension part of the forum and see if anybody has any experience with the coilovers that you plan on purchasing!