I think for moderators and the other automatic groups you’d need to use the rails workaround of Nathan’s I linked above ( Allow non-members to pm the administrator - #5 by JammyDodger ), but I think creating a new custom group for this could be easier if you’re not tied to one of the automatic ones.
(Though an excellent advocate for adding it to the UI if you fancied adding the use case to Allow email in for moderators, staff, and admins 
)
I think it should be possible to build that email address into a theme component that displays a button on the about page. 
For anons/logged out it would always open in their email, but that’s pretty close.