A 1/1 copy of Ragnaros still hits for 8, so it is a monstrous beating if Barnes happens to choose Rag out of your deck.
The computation of how good a given minion is if Barnes hits it is simple. However, whether or not Barnes should be in your deck is actually quite a complicated affair. You have to consider that the fewer minions you have, and the more specialized and expensive they are, the better Barnes is. You can definitely build some degenerate combos with just Barnes and 1 other minion. Problem is, your deck can only have one Barnes. How many suboptimal minions can you afford to put into your deck to maximize the efficacy of Barnes? How few minions can you run before your deck becomes total garbage when you *don't* happen to draw Barnes in the early going?
I have no idea! It is too complicated, even if you narrow the case down a lot. It ends up being one of those things where you simply have to play Barnes in a deck for 100 games and see what shakes out.
This is one of the things that I think people don't properly recognize about Hearthstone and other games of its ilk. You can theorycraft all you like about what cards will be good, but even really talented players who play all the time are often horrifically, hilariously wrong about cards. Barnes in particular is hard to figure out, but minions don't have to be that complicated to be tough to get a proper value on. Trump, for example, who is a very strong player and well known, famously thought that Dr. Boom would be pretty much unplayed, and then Dr. Boom went on to be one of the most broken cards ever released, and the subject of constant 'please nerf boom' threads for literally years. Dr. Boom isn't even complicated, and doesn't require special deck construction.
Despite that it is obvious that properly valuing cards requires you to play with them a lot, people still desperately cling to the opinions they develop long before ever trying to fit cards into particular decks in particular metagames.
I think it is fine and good to consider how cards might be used and to try to think of how their value might be maximized even before they are released. But we should all take a deep breath and accept that we just can't get proper valuations on cards until we have good data to work with. A healthy acceptance of the limits of our own knowledge and computational power is needed here.
Is Barnes going to see play? I am confident he will. Is he going to be nuts broken? I kind of doubt it, because balancing your deck around a single card that wants to come out in the early game is sketchy. I think one thing we can say for sure is that Barnes has sufficient randomness in his possible results that we are going to see a lot of blowouts on Youtube highlight reels featuring Barnes. My guess is that he will be sort of like Yogg was; powerful, widely used, extremely random, but not broken.
But I could be wrong because I still lack sufficient information to be sure. Important to note that.