Can you jump start a vehicle with bad alternator?

You can jump start a vehicle with a bad alternator, but it won't solve the underlying problem. The jump start will provide enough power to start the engine, but once the alternator fails to recharge the battery, the car will likely die again, especially if you don't drive it for a while. The battery will drain as it powers the car's electrical systems. Essentially, you're only delaying the inevitable. You'll need to get the alternator repaired or replaced.