Moderators have full access to gallery chatrooms provided they are a moderator on the chat server they're accessing. They can also access private rooms created by other moderators, provided they are moderators for that chatroom's parent site.
Next to the lock icon on a gallery chatroom, there's a diamond ♦ icon. The tooltip for it indicates that moderators have full access to these rooms:
It should be noted that moderators, at least in my experience, will not chat in or otherwise adjust gallery chatrooms they haven't been invited to chat in unless they have proper reason to (such as for reasons of moderation). I'm not saying this cannot or won't happen, just that it's unlikely a random moderator would use their mod status to hop in without reason.
That ♦ icon can be present on private rooms created by a moderator as well, indicating that moderators also have full access there (again, assuming they are moderators for the chatroom's parent site if it has one, see this answer for more information about SE chat privileges). Private rooms are denoted with a similar lock icon as a gallery chatroom, except with an X on the lock body: