Lots of road cars had wrapped exhausts from the factory back in the day (I'm talking 1930s-50s, using different materials and construction). Yes, thermal wrap does help considerably in keeping underhood (and above-exhaust) temperatures down. I've run with and without on the racecar. Unwrapped nearly set the fiberglass bodywork on fire. The wrapped exhaust didn't even soften the adhesive on the decals.
My understanding is that the #1 problem is that a heavy, tight wrap will restrict the tubes from expanding as they get hot, which creates stresses. I also agree with Hamish, the problem is likely to be more acute with low-quality steel. I don't know if wrapping a tube that has had a few heat cycles might be better or worse, or if an already corroded pipe might be more susceptible.
There are now looser-fitting "sleeves" on the market that are supposed to allow the tubes to expand and contract happily (and presumably "breathe" if any moisture gets in). There are also spray sealants that you can apply to keep spilled fluids from soaking into the weave. Or you could double-up with a metal heat shield or aluminized blanket over the manifold. (I sell all of these products if you can't find a source.)