Seeing that it's not listed as a destination charger on Tesla's website, I would think it's not for public use. Probably best to ask the dealership before you use to be sure.
There are a few actual free chargers in the area near there, including the quakerbridge mall if you are stuck. Found a lot of people on plug share have intentions to mooch electric rather than use the chargers when needed and as allowed.
The Princeton SC seems to be discouraging use at least (though I haven't talked to anyone there about it) as several times when I've exited that way after picking up Starbucks at Mercer Mall the end of the SC parking lot where the chargers are has been blocked by orange cones. Seems like maybe those chargers are intended for topping off delivery-ready vehicles or those in long-term service, but if anyone here has a service appointment and can ask to clarify the rules of engagement for us that would be great!