Technicaly no, you can't have a street legal one here in California. But there is some that have gotten through. If a cop stops them on the road they can call it in, weather it has plates or not and DMV will revoke the registration. Even just having a plastic tank makes it illegal as a road bike. Non DOT tires and lights that work with the engine off are other things that will do it. Some states (i'm not sure California is one of them) also require a differential in the rear- no solid axle. Having a plate and registration that says its road legal doesn't mean it actually IS road legal and it will be up to a cop to decide. Even some of the dirt bikes that got "Dually Licensed" 15-20 years ago are in danger of losing their "Road" registration if they let their reg expire and have to be re "verified".
Now days it goes off VIN. If the VIN does not come up as a bike that was manufactured for the street, no matter what you do the dmv computer will not let it be entered as anything else.
Like I said, some of them did "slip" through, but now days its all but impossible to do it - LEGALY.
My wife has been a DMV expert for over 35 years and is licensed and bonded by the state of California to do so as a private business and she has to deal with this al the time. There is exceptions though. Utility companies in rural areas can have ATV-UTV's plated for official use rural roads.
YAMAHA 450 HYBRID
85 350X- RED
85 350x -BLACK
86 350x-WHITE (with Goki)
85 250r
83 atc 70
84 atc 70
84 atc 110
09 yfz 450
2006 Arctic Cat Prowler
RZR XP 900