Yes, it supports business data in processes (which are calles "workflows" in copper).
When launching a new workflow instance, also the data for this workflow instance is passed to the engine.
The workflow can access and modify this data via a getter method (getData())
The presentation in the database is flexible.
By default copper uses standard java serialization, but it is also possible to use json, xml, or some other format.
You just have to implement interface "org.copperengine.core.persistent.Serializer".