Possibly.
Some people have suggested BPD which is a decent explanation, but I think if we really had a good chance at coming to any real conclusion we'd need to know more about Barb's life. Like, going back into her childhood, family, any predispositions and everything up until now.
Let's face it, about 99% of what we know about Barb is negatively and/or filtered through Chris or Cole, neither being the most reliable narrators for various reasons. I'm not saying Barb is secretly a shining star or even a good person, but we're obviously not getting the full story.
That's why it's a bit impossible to say. Yes, some disorders could have arose something between Chris's start as a lolcow and now or even Chris's birth and now, but if I was diagnosing her for realsies I'd want to know more and have her explain in her own words how she sees things.
However, I do think it's telling that Chris doesn't see any problems. Chris doesn't seem to understand how unpleasant and unstable Barb seems to be. Yea, he complains about how she makes him do minor shit and needs him, but he doesn't see anything wrong with her personality. He doesn't see her hoarding as an issue nor does he recognize her isolation. For most people who are around aging parents, those are red flags. There's a reason people put so much emphasis on socializing the elderly and paying attention to them. What this tells me is that Barb's behavior (illness or not) is so normalized that Chris doesn't notice how genuinely unpleasant and mentally unhealthy Barb is, most likely due to a combination of pure obliviousness on his part and growing up with it and it just getting worse and worse. We all know Chris is pretty useless, but if Chris was a normal fucking person then there could of a been a chance for Barb to get help, because even if she's not clinically unwell, she could use a professional to talk to. Sure, you can't force people into therapy and Barb is probably way to proud and lazy to go, but just having a competent son say 'hey, I've noticed you've been really unhappy these last few years and I want you to be happy again. Would you please consider seeing a therapist?' possibly could have helped and opened the door.
Now, this could all be just Barb always being an unpleasant person, not every asshole has a diagnose and fixable condition. It could totally be that failing as a parent, having no friends or hobbies and walling herself off could have majorly fucked her personality over and now she's just mentally rotting. However, I wouldn't be surprised if there is some mental illness being an influence. Note how I say influence, not responsible for shitty behavior.
But ultimately, I don't think we'll ever know 100% concretely unless Chris/ Barb tells us (and then I guarantee it will be met with skepticism, possibly rightly so) or have someone leak confidential files from a mental health professional (PROTIP: even if records did exist, don't do that. It's illegal).