Based on the definition for rescue attempt:
A rescue attempt is the effort to recover a Lost Soul from the Land of Bondage by battle. The battle is considered a rescue attempt if a Hero has access to a Lost Soul at any point in the battle.
I would say Chariot of Fire would not activate. I'm not really sure what access means though. Does it just pertain to sites? Does it also effect protection? If it changes mid-battle, does that make a difference?
Based on the definition for battle challenge:
A battle challenge may be given when there is no Lost Soul available for a Hero to rescue.
I would say Chariot of Fire would activate. Just because you don't have access doesn't mean there isn't one available.