No EAP itself doesn't store anything in the database unless you configure it to do so.
Default configuration comes with in memory H2 datasource "ExampleDB" configured but that is just to help you start with developing applications noting else.
You can remove that datasource and everything will still work.
What your application requires than, is completely up to you, if you don't need database access that is completely fine.
Thanks Tomaz, That answers my question.