Yes you can have a street plate and a green sticker. It is called dual registration Dmv sec 13.130
http://dmv.ca.gov/pubs/reg_hdbk_pdf/ch13.pdf The DMV gal will to have her manager get out the big book to find the correct codes. They never know how to do the oddball stuff.
The other advantage is you can non-op just the street plate (if you decide to cancel insurance) and still be legal off road.
If you have an amphibious car you can tripple register it with a CF sticker for water use.