I have no personal experience, but i have been told that the wrap traps in moisture and holds it against your manifold, exhaust, etc. and will accelerate oxidation/rust. Now i do not know how true that is and i have also been told that you can get a heat wrap sealant/glue that you can spray over the wrap that will seal it up and keep it from getting any moisture. Which is also something i am not certain about. Take this how you will as i have said this is just what i have heard and do not know to actually be true.
It is true, but I had a wrapped downpipe on my car for a while and I removed it after several months of use with no problems.
Wisepanda had his header wrapped aswell, no coatings on it. And we removed it with no isses. My friends 4inch downpipe ahs been wrapped for about a year now, car is daily driven, even in the rain and it was removed when he blew the motor a month ago, still mint.
IMO, as long as the metal used is fine. And you wrap it properly. It'll rust just as soon as a manifold/downpipe that is untreated.