By looking at aerial images you can clearly see there are indeed motorhomes parked up here, but whether they are allowed to park over night or not is outside the scope of OSM..

A quick google search says:
"You can park on the Drove, it's a vehicle accessible dirt track Off the 303 that runs right next to the stones. though, you're better turning in from the Larkhill end"

So, assuming they mean "Byway 12" is "the drove" and "Larkhill" is "Willoughby Rd." (And another quick google confirms that they do)  

then yeah. according to "the internet" you can park up there.

That's probably not official parking or actually signposted though, so it doesn't belong on the map.

Please utilise search engines, it took me less than 3 minutes to google that information.