Barnacles are super cool creatures! But they're not quite a replacement for gills.
This question really comes down to "how much oxygen can these barnacles reasonably extract from the water?" Fortunately, we have barnacle biologists (er, cirripedologists, if you're curious) who have studied them extensively and were kind enough to post their results online where some digging in Google Scholar turned them up.
Crisp and Southward published a paper in 1961 extensively documenting the feeding habits of barnacles. They note five different feeding patterns, recorded via stroboscopic cinefilm and suspended in a low concentration of milk. In the latter half of the paper, they discuss whether or not it's possible for the barnacle to obtain enough oxygen to survive by estimating the amount of water flow through the mantle cavity. The relevant passage is below because the article itself is paywalled (although purchasable for, cover price, 15 shillings):
The number they come up with is 0.1 liters/hour, although they concede that
"These figures are all very rough estimations because of the large errors that may have been introduced by the irregular shape of the jet aperture and
other unavoidable approximations"
So, how does the barnacle's uptake of O2 compare to your Abyssal's oxygen needs? Assuming that they have similar metabolisms to humans, we can ask NASA for an estimate of human oxygen consumption, which of course they have precise numbers for. A human living in space requires 0.84 kg of oxygen per day - apparently the same amount as required on Earth.
The last piece of the puzzle is the conversion between liters of seawater and grams of dissolved oxygen. This is another well-documented data point, and strongly dependent upon the environment. Typical measurements of dissolved oxygen in seawater range between essentially zero in anoxic zones to upwards of 20 mg/L under circumstances like algal blooms. You can play with real-world data via NOAA's World Ocean Atlas, but 10mg/L was the maximum that I found (surface ocean near the poles).
Now, this turns out to be one of those lovely problems where we can just multiply the units straight across. As a best-case estimate, a hundred barnacles could produce:
$$\frac{100\ barnacles}{Abyssal}*\frac{0.01\ g\ O_2}{liter*barnacle}*\frac{0.1\ liters}{hour}*\frac{24\ hours}{day} = \frac{2.4\ g\ O_2}{Abyssal*day}$$
That's actually not as bad as I feared! We're off by about two and a half orders of magnitude, between the 840 g/day demand and the 2.4 g/day production.
But wait, what if these Abyssals are really encrusted with barnacles? We started out with the 100 barnacle estimate as an initial guess, but that wouldn't even come close to covering a human entirely. The surface area of a human is around 2 square meters, and the footprint of a barnacle is something like 12 square centimeters. If we coated a human body in barnacles, we'd get an oxygen production rate of:
$$\frac{2 m^2}{Abyssal}*\frac{10,000\ cm^2}{m^2}*\frac{barnacle}{14\ cm^2}*\frac{0.024\ g\ O^2}{barnacle*day}=\frac{34\ g\ O_2}{Abyssal*day}$$
Darn. Still off by a good amount, although we should also be aware that this is a best-case scenario. I added a few square centimeters to the barnacle footprint to account for optimal packing and areas that you don't want encrusted, but we're still working in pretty much ideal conditions.
Time to bring out the big guns.
My other answer, about the plausibility of mermaids, discusses nudibranchs fairly extensively. These stunning critters are literally defined by the beautiful plumes they have on the surface of their bodies, used to maximize surface area and therefore gas exchange. However, many soft-bodied organisms in the ocean breathe in a similar way, some of which are parasitic.
Marine flatworms are amazing creatures. While many of them live a sedentary lifestyle, others actively swim through the sea, and still others operate as parasites. It's imaginable that a symbiosis develops between an ectoparasitic flatworm and an early ancestor of the Abyssals. I don't have hard numbers for you because estimating gas exchange rate is the worst, but a few flatworms would provide the same oxygen uptake as many barnacles. This becomes even more plausible when mechanisms like kleptoplasty come into play: a feeding strategy in which algal chloroplasts are stolen and used by the predator as a source of food and oxygen. Although only documented among the sap-sucking, solar powered, shell-less sea slugs, it's entirely plausible fiction for flatworms to have developed this trait as well.
The other advantage we can leverage here is that humans use a significant portion of our energy simply to stay warm. This is slightly dangerous territory, because we're already assuming a best-case scenario of high oxygen content and minimal metabolic effort, which are in fact inversely proportional because oxygen dissolves better in cold water. However, there are places in the ocean where the water isn't all that cold - hydrothermal vents and the misnomered cold seeps come to mind. The deep sea where these thermal vents are found also usually has the advantage of being below the oxygen minimum zone, where O2 levels return to surface concentrations. Finally, mammals in the ocean tend to be covered in a thick layer of blubber to help with thermoregulation. Your Abyssals will be much happier if they're chubby - which in turn would also increase the surface area for respiration!
So our best bet will be chubby, deep sea, spa-loving, barnacle-or-flatworm-encrusted creatures who like to hang out near hydrothermal vents. Huh, that sounds a little familiar...