I have Thermal Exhaust wrap on my Manifold - I'm all for it r.e maintaining Exhaust Gas temperature Inside the Manifold - helps reduce under bonnet temps - and increase turbo efficiency......... best of all, it looks the part
I haven't seen any issues with moisture or damage to my Manifold - I did recently replace the thermal wrap that had been on for a while - so I'm happy it won't have a negative affect for me in this regard.
I wouldn't wrap a Backbox myself - or any part of the Exhaust that would likely be as exposed to the wet - i'd expect it may cause issues with moisture retention and corrosion.
it would dampen the sound somewhat without a doubt - it would absorb soundwaves to some extent - how effective it would be
Paul.