and is there a wired connection to that connector terminal?
There is usually a terminal provided to allow for it by the
connctor's manufacturer.
Simple chassis contact is not something you'd count on for signsl,
power or safety, unless specifically designed for the purpose.
That's why the ground stud is labelled as such, and electrical
contact is made with reliable conductors.
I don't think face plates are expected to have any electrical
function - they're designed for ease of use and cosmetic values.
They can't be specifically listed as a conductor or insulator
in their safety files, unless they meet certain requirements.
Usually these stop at legibility after cleaning and flammability.
The metal or other surface they are mounted on serve the chassis
function.
Zinc/chromate passivation on steel was considered to be an excellent
conductive finish for purposes of emc control, when it was widely
in use. Current substitutes may have issues.
RL