Yes, staying at state parks is possible. I don't know the rules at all of them but we have never had trouble getting in. We are not the only ones that do this. Lots of expediters have truck-camping stories to share.
We prefer the more developed RV parks (KOA, Good Sam) for their showers and laundry. While more primitive, the state parks are a lot more fun if the woods and trails are what you want. We have parked the truck on California state beaches too and spent days there (not overnight).
The attached photos are from a state forest we stayed at near Los Angeles while waiting for freight over a three day weekend. There was no power or water hookups there and quiet time rules kept us from running the generator during certain hours.
Note that unless it is an Onan, the generators commonly found on expediter trucks would be very loud compared to what other park users would be used to. You might get some complaints, even when run during generator-OK hours.
The Freightliner picturs are from our days driving fleet owner trucks. We once had a delivery nine miles deep into a national forest in Oregon. It was a water pump going to a gold mine deeper into the woods than the truck could go. Once the front-end loader picked up the crate and disappered into the hills, we saw no reason to leave. The crew suggested we spend the night and said water from the nearby mountain stream was pure enough to drink.
That was great. Turn the key off and we were camping. The next morning we commuted from the sleeper to the cab, turned the key on, and we were working.
