I'm not sure she's prime for Birdie, especially if Chelsea knows her personally and recognizes there's a substance abuse issue rather than just affluenza. Chelsea/Birdie's all for shaming exploitation (of privilege, of those without it) but her agenda kinda rules out increasing the stigmatization of MH issues.
That being said! Maybe their parents pushed them on one another when Cecily got to NY and they found they got along? I could see Chelsea being the friend who slipped into babysitter mode at a certain point in the night. Not a total buzzkill, more felt a responsibility to hold Cecily's hair/drag her home when shit got too far out of hand?