FWIW, I've had a downpipe and turbo manifold wrapped on my car for 3 seasons. The manifold back then was a greddy log, downpipe was stainless from ATP welded by me.
My friend has a set of (mild) headers on his 340. We wrapped them 6 years ago (first things I've ever wrapped) and they are still on the car doing fine.
I honestly don't know why people are paranoid about moisture.....there'll be more moisture INSIDE your exhaust from heating and cooling - we've all seen the little puke out. Anything getting on the wrap (which BTW, most companies recommend wetting it before install so you get a tight wrap) is going to burn off because of the SMOKING hot exhaust