You are probably correct. I don't know where the point is that you will notice a weight difference.
Just weighed my PSA BO, bare, 5lbs 6oz.
8oz, which is probably unlikely given how little barrel we are talking about, would *almost* be a 10% weight reduction. It's pretty darn thick though, I'm guessing maybe 1"? Larger diameter than the gas block by an observable amount. Front seems to be right in the .72" realm, if my recollection of diameter of my other rifle forward of the block is correct.
I think the gun feels relatively heavy because it's so compact...adjusting your body to account for that means the elbows are bent sharply, and your hands are only about 8" apart given the short handguard. My 16" barreled .308 with scope and adjustable stock weighs in around 9lbs, so I can see where the weight *seems* different. Stock extended, that gun is probably a foot longer than the 300BO.
Realistically, probably not a concern at all. But I suppose if you want the lightest gun, and the price is the same, no reason not to go with the lighter barrel? I don't see an 8.5" barrel needing a whole lot of additional rigidity. :) But if you don't want to wait, you'll probably have to buy the first thing they have available. I see they are still sold out, I've noticed they have been for awhile, although the odd batch will pop up, they must not last.