Their relationship seems to me to be more emotionally intimate than you'll find in your typical nonsexual relationship. Speaking from experience (Navy security), with a male shipmate, there are some personal areas you avoid because it'd be gay. With a lesbian, you don't go there because you don't care. With an ugly girl, you only have basic interest, mostly because if you're not decent to the ugly girls, the hotties will hear about it through girl talk and won't have anything to do with you. With a cute girl, your interest is due to your sex drive trying to get you laid -- real interest in the vagaries of her life doesn't begin until you start getting the impression that she might be a keeper.
It's not an exact match for siblings, either. Tweens tend to have cruel positional battles. Teenagers are too awkward, distant, and wrapped up in themselves. Adult siblings are carrying baggage, and have lives of their own.
Rukia and Ichigo's emotional interplay is overly complex for a simple stereotype.
Ichigo is the front man.
Chad is the stalwart friend: the backbone.
Uryu and Renji serve as masculine benchmarks.
Orihime is the bumbling sidekick and adds a little unrequited attraction byplay.
Rukia is.... what? She's too complex for a sidekick. Too involved for just a friend. She's central to Ichigo's life as a Soul Reaper. Without Rukia, what is Ichigo? Just a pinball reacting to circumstance. It is Rukia who brings everything into focus and gives meaning to his life.
As for Rukia's apparent lack of romantic interest, I don't think her defenses would allow her to initiate, or to give in easily if interest was shown in her.
I don't think she'd give in to anything much short of a hero being awestruck and becoming resolute to sweep her off her feet. So, basically we're talking about either Ichigo or Renji realizing that they can't live without her, with nature then taking its course.