This is a really stupid subject and I can't believe I'm even participating.. I'm out. Blow yourselves up if you want. I'll send your family a condolence card.
I don't believe being inquisitive with a measured approach to safety is stupid at all. It's a question posed. No one is saying someone should go drink a case of beer, try this, and film it with a phone camera this weekend with no safety measures taken. If you knew how to assemble an AR upper, you too would be assured that anyone who tried this wouldn't "blow themselves up." They may damage their equipment, and there is a remote chance of ancillary injury by a barrel careening off the front of the gun (most likely outcome IMO), but the rifle won't explode. As HiBC said, a barrel nut has nothing to do with headspace on an AR. Once the round is actually chambered, the bolt is locked to the barrel extension. It is as safe to fire as it would be with the barrel nut in the context of case head support.
Will it fail to fire?
Will the barrel fall off?
Will the case rupture?
Will it work just fine?
Will the barrel extension and threaded receiver boss explode, due to being unsupported?
Will the ... fill-in-the-blank ... cause ... fill-in-the-blank ... to ... fill-in-the-blank?...?
Let's assume you have ensured that there is a round chambered and the bolt is in battery. It would maybe require you to hold the barrel to keep it from being pushed out of the receiver as the round chambers. Once at that point...
Will it fail to fire? Maybe. I don't think so but there's a remote chance the hammer hitting the firing pin would push the whole barrel/bolt/carrier assembly forward. I think the mass of the barrel would hold it in place well enough for the primer to ignite.
Will the barrel fall off?This is the most likely adverse affect, is that the barrel falls off to the front. It should be safe until the bolt unlocks as pressure will push the bullet down the barrel, but it will also push back on the bolt holding it in place. Once the bolt unlocks there is a chance that the gas pressure will push the bolt carrier back along with pushing the barrel forward... possibly enough that it falls off the front. I don't know for sure.
Will the case rupture? No, the case is completely supported by the bolt locked into the barrel extension.
Will it work just fine? To get one round downrange, after it was chambered with aid, likely. I believe that the barrel may fall off (or at least be moved forward in the receiver) once the bolt unlocks, but if not then almost definitely when the bolt pushes the next round onto the feedramp.
Will the barrel extension and threaded receiver boss explode, due to being unsupported?No the chamber is bearing that outward pressure during the firing of the round. The only pressure on the barrel extension is rearward via the bolt locking lugs engaged with the lugs in the extension.
Will the ... fill-in-the-blank ... cause ... fill-in-the-blank ... to ... fill-in-the-blank?...? My guess is you aid in chambering one round, it fires, and when the next round is stripped from the mag and hits the feed ramp it will shove the barrel forward some, which will absorb enough energy that the bolt will never go into battery with the new round.
Looking at it, rotational force placed on the barrel due to rifling could also cant the barrel and bind it so that the bolt may not unlock properly (or really at all). I now have a strange desire to see this done. If I had random disposable income a video would be forthcoming. But I don't. And I have mouths to feed. So, single rich guys up!