I see a couple of issues:
1 - Most auto battery chargers are "trickle" chargers. They slowly restore the charge on the battery. It's very possible to drain the battery even if it's on the charger by using more huice than the charger can replenish.
2 - Decent home audio hardware is cheaper than decent car audio hardware.
3 - This setup would look ugly as sin.
4 - You would be the laughing stock of your dorm for this setup.