Can you get a campsite for 19 foot van (no power needed) without making a reservation--just by arriving one day and getting a spot?

Maybe, but I would not go without reservation.

Strongly recommend a reservation. During peak season reservations fill up at least 90 days in advance and that was for weekdays!

Seems unlikely since you have to make reservations online and that specific campground is always in high demand due to amazing location. Maybe off season it is possible ...