No. Puncturing a satellite's battery would not likely help it deorbit faster. Satellites maintain orbit through a combination of factors such as orbital mechanics, propulsion systems, and atmospheric drag. While battery power is vital for satellite operations, it does not directly influence the rate of orbital decay or reentry. Controlled deorbiting maneuvers typically involve specialized propulsion systems or atmospheric drag techniques to gradually lower the satellite's orbit until it safely enters the Earth's atmosphere and disintegrates. Puncturing the battery would not effectively alter these orbital mechanics or contribute significantly to a faster deorbiting process.