As a Las Vegas resident, I wouldn't even consider camping at Atlatl in early June, so you may have a good chance.... expect that it will be over 100F when you get in and will only cool to about 90 during the night.

I couldn't say, for certain. We were there in mid May and many of the sites were occupied. We arrived before noon and were surprised to find a water/electric site vacant. However, it was early in the week. I'd say, on a Friday later in the day, you won't likely find an empty campsite. On the other hand, I don't think it would be too terribly hot yet.

You might be okay only due to the fact that it will be 2 degrees cooler than the surface of the sun. Summer time you have a much better chance of getting a spot due to the heat. A secondary choice is to stay at Clark County Shooting Range (about an hour away) where you can reserve a spot and have full hook-ups. What you might want to do is stay at Clark County Shooting Range the night before, get up early and get to The Valley of Fire by 8am or 9am the next day. Here is their web site: https://web2.myvscloud.com/wbwsc/nvclarkctywt.wsc/search.html?SessionID=ff6581d4b69b9c6bcfb2f3c430ec36cbcf8ad5a22c1d16d638dd8df7786ccc9a31c3ce4f0d2fc82350f2964c70c3aa53cdef8729462750998c8a2a8f18e748c4

We were only there in January, arriving Sunday evening, and got the only hookup site left. From what I’ve heard, it’s crazy busy during peak season, with people driving around the campground early in the morning trying to see who’s packing up to leave. I would expect the chances of getting ANY space on a Friday night to be nil, but really don’t know.

Unfortunately arriving anywhere at 5-6pm with first come first served gives you slim to no pickings, that's worse at Atlatl. We arrived at 10am and waited for someone to pull out to make sure we had a space. We are 45' which makes it extra difficult, but still you could probably get a non-hookup site and move at 9am when the early birds leave.