I beleive so, but in Ca, non-operational is totally non-operational. If you are caught driving it, even to the DMV to get it registered again, it is imediately impounded and you are on the hook for all the normal registration fees plus the penalties. So example, if you non-op register your car for two years, then get busted in the third driving it around, you are now paying 160% of year one, 80% of year two, and up to 60% for the current year in penatly fees, plus the actual registration for each year.
You also cannot park it anywhere on public property, like streets, parking lots, etc. And some counties like Riverside County in Ca have an extra thing called "Blight". Meaning if I park my crusty beat up buck on my driveway for the whole neighborhood to see, they can complain if I do not try to make an effort to cover it. The city can then require me to move it, cover it, or require me to pay fines, $150 for 1st ticket, 300 for next and 600 for every ticket after that. The time between tickets has to be at least 7 days though.