Is it possible to allow an author user the ability to set a custom property (or workflow) to a folder in the DAM?
i.e. can I create a custom property "Approved" against a DAM folder and expose it via the UI (or update it via a workflow)
I want to apply to an entire folder (not single or multiple assets)
yes it is possible to add custom property to dam and workflow. To add custom property to dam asset you have to override "/libs/dam/components/asseteditor" form page in your application.
also you can refer - http://dev.day.com/docs/en/cq/current/dam/customizing_and_extendingcq5dam.html
To add custom property in workflow you have to create custom workflow component using sling resource super type as "cq/workflow/components/model/process" and add custom property in dialog. you can take example of existing workflow under /libs/wcm/workflow area.
also you can refer - http://dev.day.com/docs/en/cq/current/workflows/wf-extending.html