At this time, it is not possible in the API available for Chimpegration to add an Appeal. (This is an option in Chimpegration Classic from within the database view of Raiser's Edge).
However, you can opt to use one of the available fields (such as a Custom Field or an Action) to add everyone sent into Raiser's Edge NXT. Once you've added that information to Raiser's Edge, you can then create a query of those constituents and then use the tools available in Raiser's Edge database view to globally add the Appeal to your constituents.
For more information, you can read about the options available for Managing Campaigns in Chimpegration here and in Chimpegration Classic here. You may also find this Knowledgebase article helpful as it describes how to work with Appeals to track giving related to your Mailchimp emails.