So the girl hasn't actually accepted your confession and agreed to date you yet and you are asking her to spend the night? That's a bit forward... (Granted, it is very clear that Airi is head over heals for her even if she's lying through her teeth about who she actually is...)
This is an interesting twist on the mistaken identity theme. I would have expected that the twin would have actually been in love with the sempai instead of trying to set up her fellow coworker with her. That makes the duplicity slightly more palatable, since Airi is trying to "protect sempai's love" for Himari by pretending to be her... Yeah... right... If she was really trying to protect her, she would let her down easy and walk away. Nope. She's fallen hard and doesn't want to give her up! LOL
You are right airi falls for sempai, this page says all:
http://dynasty-scans.com/chapters/futakaku_kankei_ch02#21
