Can hydrochloric acid vapors corrode nearby metal items?
Yes.  I used to keep my acid in a large container along with some paint thinners and removers.  Even with the acid bottle tightly sealed, the metal paint thinner containers rusted after a couple of weeks.  Will enough vapors get at your ducts to rust them?  Can't say, but it's worth the effort to wrap them.  Sounds like your major problems will be containing the acid so it doesn't reach the floor and neutralizing it without flooding the inside.