There were regular cars that made it to the trail head, so it's possible to make it. Saw a couple bike riders come in as well over the road and then take the trail towards White Mountain Peak.
Take it slow and you may or may not make it.
I've been on rougher roads and the 1st half isn't that bad. The second half gets pretty rough and even going slow, I assume regular cars might hear a lot of scraping.
