I disagree with the theory that the haibane committed suicide in their past life...
I do agree however, that their names (which are influenced by their dreams) play an important role in the story.

reki's = to be run over / stepping stone
rakka's = fall / involved nut

I think the names just serve to provide dichotomous contrast between "good" and "bad" applied to a social context...
Rakka shines when she displays the qualities of an "involved nut" in the same way that reki displays her ability to be a "stepping stone" (she took care of the young feathers and was a model figure in many ways). I don't think the two necessarily cancel each other out; both can be true at the same time.

Rather, I think the two names represent two sides of a character, a choice they get to make.

One of the most important aspects to the reki plot was that she was obsessed about her dream and her inability to remember it. Eventually, this caused her to spiraled down in a depressive cycle

This may be interpreted as her attachment and perseverance on the negative aspects of herself...

Art and media likewise, are often a projection of the author/artist's inner thoughts... which leads me to question where ABe drew his inspirations for haibane renmei from... did he himself have a depressive episode, or did someone close to him experience something similar? Once again, I don't think the entire series was about "depression" but I think it does play into one aspect of it...

If someone did ask me though, I would say that the series was about "learning to fall and pick yourself up again"
This is exactly what happened to both rakka and reki (perhaps the crow was someone who intended to help rakka, but she pushed him/her away?).