Let us first define, "Gallery" refers generally to the whole Zenphoto installation in Zenphoto terms, we are actually talking about "(toplevel) albums".
http://www.zenphoto.org/2008/08/zenphoto-glossary/
So yes, it is possible to assign a toplevel to one specific user for them to maintain.
http://www.zenphoto.org/2008/07/an-overview-of-zenphoto-users/
It is also possible to register yourself using the register_user plugin.
http://www.zenphoto.org/documentation/plugins/_plugins---register_user.php.html