Gateway drug lol, honestly i think Klein may act like the oblivious fool towards her that Kirito sees and without realizing the irony feels pity for him.
Or at least that is what i was thinking before finishing playing, now after a few things i think Klein and Alice will go either of 2 routes: either he "saves" her at some point and they get together (obviously she gets cucked later xD) or he "protects" her from others by "acting" like a criminal, i mean he isn't gropping her because he is a pervert! No sir! Its all because they are undercover! Stuff like that xD
My guess is that he will exit the story later but it will be part of the plot all along, like he will be the "villain" that Kirito gets to take down so he feels he has won and overlook Inoda, also the plots will combine, all 3 (Asuna, Sugu and Alice's) mostly because of the investigation.