The "instructions" indicate that after the initial fermentation, the wort should transfered to a second vessel at which point the champagne yeast is added. My understanding of yeast and fermentation is that it is an aerobic process yet the "instructions" did not say to aerate. I am still seeing no activity which leads me to believe there may not be enough O2. The OG was 1.084 and after four weeks was stable at 1.020 for four days. Thank you for your advice!
Yeast can function both aerobically and anaerobically. The good ol' fermentation that we know and love is an anaerobic process. What they required oxygen for is making sterols and lipds, which they use to strengthen their cell walls, allowing for reproduction. This is why a shortage of oxygen can lead to fermentation problems, because you end up too few yeast, or yeast whose health is somewhat compromised. Side note, one of the dry yeast manufacturers claims they propagate their yeast in a way where they build up their sterol reserves to a point where you don't need to aerate your wort because the yeast don't actually need more to propagate normally. Side note number two, you can actually forego oxygen and use a tiny drop of olive oil to accomplish the same goal. Instead of synthesizing the sterols, the yeast just absorb what they need from the olive oil.
Anyways, all that having been said, the reason why oxygenating after alcohol is present is that while oxygen and yeast get along great, oxygen and alcohol results in oxidation, which reduces the flavor stability of the beer and leads to flavors such as wet cardboard and musty basement.
While it is true that active yeast may take up some of the O2 you add, some of it will also react with your beer and result in oxidation. I think it was vinny from russian river that commented in an interview that people tend to overestimate how much the yeast will protect you from oxygen, and that was just in the situation of bottling, where you're not intentionally adding O2.
Lastly, I will say that the fact that its a barley wine means that oxidative notes are actually be an acceptable characteristic of the style (they're usually picked up through aging rather than oxygenating, so there is that small detail). Not saying you should intentionally try to oxidize the beer, but in this case, if you did, it wouldn't be as much of a problem as if you did it to a plisner or a pale ale, for example.
