To me, physical attractiveness of a character is not very important, and it's very fortunate, because I'm generally very turned off by conventional beauty criteria, whether Western or Eastern; so if that was important to me.. I would be left with very few comics to read.
However, I do read more stories with non-conventionally beautiful people, but I don't think it's due to the fact I find them more attractive. Rather, I feel there is a tendency for stories that escape conventional beauty, to also escape conventions in a more general sense.
I think @punkarsenic 's comic is a very good example; as the unconventional characters fit so well in the unconventional art, story etc. I don't really imagine this story, with this art, with characters looking conventionally pretty.
The only case when unattractive characters can put me off badly, is when the artist exaggerates traits to make a character attractive, but it completely backfires. Exaggeratedly gendered traits being the worst. If your men and women look like being from two different species, I'm out.
In the case of my characters, I did not think of it at all for most. Most are teenagers and probably younger than my readers, so I did not aim to make them attractive really. I don't think they are particularity attractive or repulsive to the reader? There's one of the adults who got a few compliments, though 
In your case @Tanako , I don't think Braylin is particularity unattractive physically, but certainly unconventional, and his personality is very unattractive. This being said, in my opinion, it what makes your story interesting.
I'll be honest, it's really not the type of story I usually like, and I'm not subscribed to it, but I read it from time to time because I'm intrigued by this character. I'd like to see what you have to tell us about him, I'd like to see what explanations you could give to make him more likable. To me, it's an unlikable character that I would like to be able to like, you see? To read more to understand. I really like the idea that he may appear ugly to people at first sight, but that is not actually where the real ugliness is. And how we're given the hope that, the same way that he is not physically ugly if we don't follow arbitrary social conventions, he may not have such a ugly personality if we one day understand where he is coming from.
So maybe you have a very good compromise here: a general setting and story outline that are pretty conventional for the genre and may attract the usual public, + an unconventional (on many aspects) character who may interest a different set of readers.