Can a dead battery cause my car to sputter then die while driving it?

Hello, a battery light being illuminated is a sign the charging system has failed -- not that the battery itself is at fault. You say the alternator is good -- how did you test it? How many amps is it putting out? How many volts? I would pretty nearly guarantee that you have an alternator problem, be it internally or the wiring at the alternator. Check all battery and cabling connections as well. Good luck.