I'd think not.  The neck is pretty ruggedly built and the body (of course) doesn't need humidification.  Adding humidity may do more damage than good.

Stainless steel has both chromium and molybdenum to stem corrosion.  Carbon content affects corrosion too.  More carbon generally means the steel is harder, but also increases susceptibility to corrosion.  I'm not sure of the type of steel in Gretsch's resonator.  Apologies for the geek moment.

I really like the Gretch resonators.  I want one too, by the way.  :)

Let us know how you like it!