Hi, The thing he did with her purse, that was wicked.
Would the sentence have been incorrect if I the comma wasn't there? Yes, it would. Then 'that was wicked' would be a subordinate clause, and there would be no main clause, no main verb.
Yes, it would be incorrect without the comma. As it is, while you're hear this said, I would be surprised to see it in anything other than the most casual writing.