On their recent Haven trip, they were near the edge of the site and the touring field even had its own entrance and Reception.
From what we saw/heard, they seemed to keep themselves to themselves, mostly. Although they apparently spent a bit of time at the pool, it might not have been all of them. With the onsite restaurant, they probably went when it was quieter and sat in a corner, out of the way. Apart from that, they seemed to be either inside the caravan or offsite somewhere.
Can you do Disney without completely immersing yourself in the whole experience though?
They do know how to keep a low profile if they want to, but Disney is very different to Haven, even ignoring the fact that he has to get through US immigration before setting foot in the park.