Is the Creme de Cocoa *absolutely* necessary? Will leaving it out make the ice cream churn incorrectly or will it just slightly alter the flavor?

No, it's not absolutely necessary. Alcohol lowers the freezing point so it prevents the ice cream from getting too hard in the freezer (somewhat), but you can certainly skip it and just either take it out a few minutes before serving it, or serve it straight from the ice cream freezer.