We did it recently with just the car , ( ford Ranger) right up to palm valley at the end of the track,went pass the camp site, the river was dry at the time so we had several soft deep sand crossings across the Finke.
if you are confident with traveling through soft sand with a caravan, go for it, but while we were there we had to help pull a caravan back out off the river bed, { that was a off roader being pulled with a land cruiser. Safer with another vehicle if you get bogged in the sand.
Good luck beautiful up there.
Pomme.

I towed a camper trailer into Palm valley a year ago with no hassle at all.Good camp ground at palm Valley.The ranger there may visit and offer a talk about the area.This may occur in the evening .Leave your van at the camp area and 4x4 into Palm valley.This is a bit of fun but easily do able. I went over to Glen Helen the road was corrigated for 40 odd kls on the back road towards kings Canyon.then at the T junction you turn right...bitumen the rest of the way.Opposit Glen Helen is a place called "2 mile" it is a top billabong free camping ...spend a few days there. It is an easy drive back to Alice Springs and you can call into all the gorges on the way . Ps I remember at palm valley there was a large caravan.collect and carry in firewood as no collecting when in the park area.Enjoy ..we did
Les