No, they can't kill you.
When you have a panic attack you can be absoluely terrified and believe that something terrible is going to happen to you, however, they are not dangerous at all. A panic attack is just your body's way of trying to protect you from what it percieves to be a harmful situation - even if that situation is not harmful, i.e. crowded place, train, plane, etc. When you have a panic attack your body goes into fight of flight mode, which means that it is preparing your body to protect you from a harmful event, this means that blood is directed away from your organs and sent to yours muscles so that you can run or fight more efficiently - this can be why you feel sick, light headed or 'off balance', your heart rate also increases (again to prepare you for fight or flight) and you get an adrenaline rush which can cause you to feel shakey or achey - this is why it is important to exercise reguarly if you suffer from anxiety. Another reason exercise is important is that it makes you feel happy! None of these occurances are the least bit dangerous, just unpleasant. I find that knowing the reasons behind the symptoms that you experience during a panic attack is helpful in rationalising them and feeling safer.