He was already stuck inside with her, thanks to her emotional blackmail, "please don't go outside, I am scared if you go, I will eat all the food." She has already done that to him once that we know of, and I would bet she has done it since too.
In the beginning I was extremely unsympathetic about both of them, but after watching some of their old videos(its very boring in lockdown here), I am actually a bit more sympathetic towards Gene. He wants to do things, he wants to go out, he wants to join a band, he wants to travel, and he seems to want Jen to do them too. Do I believe he loves her as a girlfriend? No, but I think he does care about her.
Saying that though, even if Gene does want to get sober, Jen won't let that happen, they are supposed to be beating their addictions together, but we all know that Jen doesn't want to stop eating, and because of this, she won't let Gene get sober, because a sober Gene means Gene is going to start looking for something better, not only that, but she is sharing her own addiction with him.
Its actually pretty nasty, but then again, Jen is grade A nasty.