Hi,
the Ecosystem stores everything in your Assets Folder of the project you are in currently when browsing, there is no hidden library folder somewhere else unlike the AssetStore, so you are safe to simply copy your project, you'll get everything with it.
However, once offline, you can't get anything more than what you had downloaded, there is no "caching".
Is there any reasons why you don't want to be online when working with Unity? It seems odd.
Bye,
Jean