From the REG:
Rescuer’s Choice
Before a player begins a rescue attempt, he must announce which Lost Soul he is trying to rescue. That is the only Lost Soul he is eligible to rescue. If that particular Lost Soul is taken out of play prior to the end of the battle (by Burial, Son of God, or New Jerusalem), then the rescuer will not rescue a Lost Soul even if his forces win the battle.
I would say no based on the description in the REG. It is removed from play before the end of battle. Also, when cards hit deck they clear, so I do not believe that you could say that it is the 'same' soul you were starting to rescue.
