(Short answer): No. An anxiety attack or a panic attack can not kill you.
(Longer answer): But (studies do show) that a pattern of years and years of anxiety or panic attacks (which causes a life of high-stress) can increase your chance of heart problems (when you are a lot older).
Just think of it as high stress. In the short run (and the medium-run), it won't hurt you.
But in the very long-run, years of high stress could.
Thats scientifically backed up--
So will a single panic attack hurt you. Not at all.
But will years and years of anxiety problems and resulting high-stress hurt you? Maybe.
**If your panic attacks are social in nature (due to social anxiety or social phobia problems, which I have) here is a good self-help resource (that has helped me a lot)-- "Twelve Gentle Steps to Overcoming Social Anxiety"