2001 Dodge Stratus r/t

Ill try and do the best of my knowledge here, thanks in advanced. I am interested in a 2001 dodge stratus r/t, 3.0, 6cyl (mitsubishi engine) coupe with 51,000 miles, its at a salvage yard, it has burn damage on the inside, it seems to be ok everywhere else, except for the battery, ok well the dealer boosted, and it cranked well, after drving down the road, and on the decelleration it died, well we boosted if off again and it worked fine, but everytime the rpm's lower, it dies. Now I understand that the fire may have done damage to some wire and its probally the cause of the batter drainage, but my question is would a bad battery make a car die. I know older cars you could crank up the car and take the battery off and it would still run, but he was sure that it was the battery, and to me it kind of makes sense, if the computer doesnt get any juice, along with all the other components, then the engine shuts off, I was just wondering if DEAD battery would cause the car to die.