There is no definitive answer to this question. It depends on the wiki, their community, and their admins. If the community agrees to this policy, you can do it.
In reference to the specific question, I don't see how you could sockpuppet on chat without sockpuppeting in general. As a recommendation, I would block a user for a short time (1 week or around that) for abusing chat, but with increasing times (along with a warning on their message wall/talk page) if they continue to offend.
Agreed. Shorter bans are often better and are a better way to convey the message. There's always room for change within a user! As Fandy said, blocking them from the entire wiki depends on the severity of the offense. If the user still makes good contributions to the wiki, or makes no contributions to the wiki then a block isn't necessary. If he is socking, then a block or indeed an IP block is necessary.