Yes, of course its possible for more than the obvious reasons but, rather unlikely as the primary cause suggested but, certainly may initiate a secondary cause as someone has mentioned re spasm and might also cause shock or even damage a (weak) blood vessel causing bleeding. read more
If its big and gets stuck you can choke to death possible because it takes some time for it to melt. Just put pressure on it and try and swallow it as best you can with water. It does depend on its size like for example if its big there's more chances of it getting stuck in your esophagus. read more