My research indicates that SCCM 2012 must be installed on a server that is a member of an Active Directory domain. Does that mean that Patch Manager must also be installed in a domain?
No, as long as Patch Manager can talk to the Site Server and Software Update Point it should be fine; no need for the Patch Manager server to be in a domain. You *do* need to make sure that there are proper credentials specified in the Credential Ring for the site server and update services server (SUP).