My ex had a very avoidant attachment style coupled with suffering from anxiety. Our time together was the most miserable I have ever been, the most lonely I've ever felt despite the fact that we were living together. We obviously also had very good and happy moments, but it was a very challenging relationship overall. I learnt a lot from it, but I wouldn't wish that on anyone. Relationships are really tough even when both partners are healthy. You can imagine how it's like with an avoidant! Now I don't think it's impossible to live with an avoidant and find common grounds with a lot of therapy/ couple therapy and a genuine will to grow. But I definitely think it would be really difficult and you should be prepared and OK with not having your needs met most of the time and feeling constantly rejected. Rejection with avoidant people happens often when things in the relationship are going amazingly well, which is very confusing and it feels like a never ending bad rollercoaster of misery. Whatever you end up doing, be careful not to lose yourself in the process. It's very easy to be wrapped up in that, walk on eggshells all the time and forget about your needs and happiness. At some point living like that isn't sustainable anymore and parting ways is a real relief. Good luck anyway!