I feel like Pepper is one of those people who, when sick, goes into social isolation. When we had a random unrelated-to-plot flu outbreak in the Ministry last year he relegated himself to the couch and bathroom - consciously he told himself it was so he wouldn't bother Jo overnight but I suspect quite a bit of it was this secret need to be in his own space, away from people.
If the DEs had never taken over the Ministry-- well, he wouldn't be going through alcohol withdrawal to start with, but if there
was a situation where he still had his flat with Jo and he was going through withdrawal, he would be very, very stubbornly refusing to accept Aloysius' offer to stay there. He has a lot of pride and grit and determination when he wants to and he would be very set about just bunking down in their flat and staying there until either he was better or he failed.
Being at camp is where it gets extra interesting though, because he's not just alone with Jo. Half the ex-DMLE is there too, in a very social-living environment, and these are not all his close friends. In fact, very few of them are particularly close to him, and even those ones he does tend to hold at arm's distance - in the Kate/Pepper log she observed that their friendship is not based on sharing intimate details about their lives, despite the fact that they'd been intimate. And he would very much hate to have people he doesn't know very well and doesn't like, and who don't like him, wandering around nearby when he's at such a low point. It would make him feel very, very vulnerable.
So his decision, essentially, on whether to retreat to Aloysius' basement, is a battle of different kinds of pride - whether to let Aloysius "win", and do something that feels like an admission of failure, need, incapability, and to put himself in a position where he's essentially relying on someone he
hasn't before (which I could elaborate on an awful lot, actually; his relationship with Aloysius is so, so different to Jo or Mill), or to do it on his own but allow an awful lot of people to see him in a very weak position.
And, yes, ultimately it's inevitable that he'll relent to the lesser of two evils and give in to Aloysius. It'll probably be strange for him because I think in the past he's subconsciously figured.... hm, how to word this. He considers himself more independent in the relationship than Aloysius probably does. Like his frustrated "I didn't ask you to worry!", he has gone past the point where it's a relationship of momentary amusement and convenience, but he hasn't reached the mutual absolute trust he has with Jo and he definitely doesn't feel the sort-of-submission he did with Mill. So letting/making himself rely on Aloysius for basically the first time? Going to actually be a bit nervy for him, I think.