You better join, later Blake will say you are unofficial or free member, just to her, to the Brotherhood you are not listed at all.
yea but idk if there's much significance to the story yet
the mc's goal and why he considered joining the brotherhood in the first place is because he need protection. now that he's somewhat part of the high order (if Claire get the authority back) he doesn't really need the brotherhood the only thing it may affect probably is the dialogues or the love path with blake