I don't think he should, because, right now, Rachel is the objective of the comic (ike it or not), and Baam saying yes to Androssi would implie he doesn't care much about her anymore, thus the comics loses sense. At least for me.
Actualy, what you're saying doesn't make sense. Baam used to see Rachel as his savior, she was all he knew and he wanted her back, he wanted her safe, he wanted her wish fullfiled. But then she tried to kill him, and there is no doubt Baam will on or offscreen be filled out by Koon as to what she did.
Baam no longer searches for Rachel because of those reasons, but because he wants answers. A romantic relationship doesn't mean dropping an interest in anything women related.
Because Baam actually hasn't shown any intentions for romance and it's only one-sided for Androssi, same for the other girls too.
Poor analogy on my part. Let us say I like a girl and told all my friends we are dating, it doesn't mean it's true and we are together currently. When the girl is aware of the self-claimed relationship I have with her, she will probably reject me and things will be quite awkward for now on.
Doesn't mean he can't start showing it. Wants to try it out, maybe is interested, maybe he is just curious to what it is and ends up liking it...
I mean, what's wrong with a relationship starting midstory and then staying like that for the rest of the story? Why don't we ever see that? Why is it so hard for authors to include romance for their MCs in stories that are not pure romance/slice of life?
You know what I loved about Sword Art Online? (I also denounce the existance of everything after episode 14). THE RELATIONSHIP THAT STARTS IN THE MIDDLE OF THE SHOW! MC BEING CAPABLE OF ROMANTIC LOVE! I think it gave a lot of quality and took off a lot of potential frustration over "another MC incapable of love".