Right from the beginning of TDI, it was made quite obvious that Courtney is a fierce competitor; remember when she talked to the camera while the Gophers were having their hot tub party, and vowed that she'd win the whole thing. Courtney gets angry when her buttons get pushed, she has always been that way; but in her return episode, she was put on the team opposite Duncan, and with four losers, who were acting like bigger losers than usual. Her craziness is what alienated her from her other teammates, but if it wasn't for her, they had no chance at all.
I expect Courtney is going to stay around for a while, at least until the teams are dissolved and she reunites with Duncan; and as a team they'll get further. I don't think she'll win, I think her competitive attitude is turning the others off; like how Heather's scheming alienated everyone in TDI, and ultimately the remaining campers (Gwen and Owen) ganged up on her.