We have stayed at non-booking sites a couple of times. The first one (Fisherground, Lake District) we went off-season so it wasn't a problem; the owners told us they filled up very quickly on bank holidays/summer hols. The second one (Pinewoods, Norfolk) we went on a hot July weekend but had friends who arrived first and were able to save us a space.
If it's a really popular site I would plan to arrive early in the morning (pre-9am). Find out what time pitches have to be vacated by and be prepared to hang around waiting for someone to leave. And have a back-up plan! What site/area are you looking at? Most non-booking sites ime don't have marked pitches so I wouldn't expect the owners to hold any space for you.
in our experience, if it's a really good site and popular on review sites (eg talked about here and ukcamping) then it could book up for the entire school holiday period months in advance. So yep, I'd give them a ring now!
How does that work? I've seen a lovely site that's 4-5 hours drive away that I'd like to go to in the summer holidays. Do I phone in the morning to see if there's space? Will they hold a pitch for me if I let them know I'm setting off? I don't really fancy having to search for an alternative after 5 hours in the car with DS.