Yes, but make sure you have some gear to leave at camp so no jerks can easily poach your fcfs spot. I've seen it before at other high demand fcfs camps
You can sleep in your car if you want to.
We stayed at this campground in July 2018 and the site next to us did not have a tent and slept in their vehicle. The host did mention that the concern is when nothing, like chairs or other gear, is left at the site when exploring the park. If nothing is left in the site it can appear to be available for others to use and can lead to disagreement of whose spot it really is. According to the NPS site, https://www.nps.gov/yose/planyourvisit/nrcamping.htm , you can sleep in your vehicle if you are in a spot that allows it. My recommendation would be to confirm with the camp host upon arrival and make sure you have something like chairs or other gear you can leave for the day, if you choose to explore the beautiful park.
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