No, you are looking at it wrong. Jack didn't need to be alive for their plan to work. They already have the doctored footage to plant in the surveillance camera. They kill Tony, Michelle, and Chloe, then kill Palmer and plant the footage. All of a sudden, CTU is searching for a guy they think is dead. Even if Jack really were dead, CTU would be searching high and low for him. It's just a plus that Bauer is alive.
But how did they know the four that knew jack was still alive? Also they killed palmer and michelle and would have gotten tony if they had left together But they send goons to capture chloe?
Thanks for the link, appreciate it.