Yes, but it is tough to do.
A Bear Hug prevents the person from inhaling, or from inhaling deeply. If you can squeeze tight enough then you can force the person to pass out from lack of air. However, once you let go the person will start breathing again. A Bear Hug would only be fatal if you were strong enough to seriously restrict their breathing and then only if you held it on for quite a while after they passed out.
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