The Host and Producer have similar abilities when joining their Enterprise Studio.
A Producer, even when part of the Enterprise team, does not record a separated track.
A Producer with their mic/camera enabled during a recording does appear on the Internet backup track.
If you join an Enterprise Studio using a Producer invite link but you are not logged in as part the Enterprise team:
You will not be able to start and stop the recording;
You will not have access to view/download files after a recording;
You will not bypass the waiting room when entering the Studio (if a waiting room is enabled).