I tested this on a current self-hosted instance.
Staged users are not members of trust_level_0, so having trust_level_0 in skip review media groups does not exempt them.
However, adding logged_in_users to skip review media groups does.
I tested this both directly against NewPostManager and through the real email-in path. An email from a newly-created staged user containing embedded media was posted immediately instead of going to the review queue.
So for a helpdesk-style setup where arbitrary new senders are created as staged users, adding logged_in_users appears to provide the intended behaviour without needing to activate the users or maintain a separate group.
One slightly surprising detail is that staged users match the logged_in_users pseudo-group for this check even though they are not activated/logged-in accounts in the usual sense.