Correction- Brooklyn isn't homeless in this show, so why would she dress as if she were?
Streetsinger IS homeless, and I have seen homeless people in this city (NYC) who dress eerily similar. Especially that trenchcoat covered in buttons/mirrors.
Also, because these streetsingers live underneath the Brooklyn Bridge, in what appears to be a never-ending construction zone, I think it's wonderful that all of the costumes are made NOT NECESSARILY from trash, but from objects you'd find on the street or on a construction site. The idea is that the borough of Brooklyn is such a huge part of their lives that it even creeps into what they wear.
I especially love Paradice's bubble wrap stole. It lends itself perfectly to when she says "I've heard some rumblings about me..." and proceeds to stomp on the bubble wrap.
And no, I don't think this costuming is weird. It may not be what some consider the "norm" but what is? Saris under a fountain? A green witch on a broomstick? A straight man playing a Nazi-era transvestite in a skirt suit and pearls?
http://preppylife.tumblr.com/