I rode it this morning. No problems. There is one section of about 15 feet where the road is completely washed away and you must ride a very narrow dirt track, but otherwise it's all paved and in fair shape.
I passed a few rangers today, so you shouldn't have any problems. The road is closed to cars (and impassable for cars due to the worst washout), but is on public land and should be open for all. There were a few other bikers, some runners, and some dog walkers out today.
Since the road is closed and impassable for cars, you should so essentially no traffic between Martinez and Crockett. Well, maybe a car or two near Port Costa, and some people heading to or from the makeshift trailhead at the start of the closed section near Martinez.
A wonderful ride, I strongly recommend it.