Short answer is yes.
(Not guaranteed, so test on a local machine, with dummy users, and dummy moderators.)
You may need to create the folder first, so you can put the new forum in it.
Phorum Admin / Create Forum
Create the forum, remove permissions for public and registered users.
Phorum Admin / Edit Group
Create a group.
Assign permissions to the group for the forum you choose to add in the drop down list.
Phorum Admin / Edit Users
Locate the member that is a moderator.
Click on their display name. At the bottom of the page that appears, you can add them to a group.
Admins will be able to interact with the forum in any case.
Unless it has been fixed, you must have 0, or 2+ groups else the admin user search does not work.
Test with your dummy users, to see what may be seen.
1 public (not a member)
1 registered member not logged in
1 registered member logged in
1 registered member who is a moderator
1 admin
Disable or delete dummy users when finished testing.