That's a local decision. Upstate clearly doesn't want these camps so I don't see why they wouldn't enforce the closure.
Not sure how you are defining "upstate". These are local decisions made by the various counties that the camps are located in. Many of the camps are in Sullivan County (Monticello), others are in Orange, Dutchess, Ulster and Chenango. Each County has its own Department of Health which oversees the camps in its County. The local Sheriff's Department will be the entity that has to police and shut down an illegally operating camp and I don't know if each County feels strongly against or for the opening. These are big money makers for some of the smaller counties.
Of course, none of these camps can open legally without NY's Dept of Health giving the green light for sleep away camps, but all the enforcement will be on the local (County) level.
Meanwhile their attempt to get a TRO allowing them to open just took another small step forward as they asked the Judge to give them a hearing on June 25 (letter attached). However since that is the day that they claim that they want to open, I don't know how they convince a Judge that the TRO will give them any real relief as he will probably be skeptical about their ability to safely and quickly open if he allows them to do so.