Right now this is not built, but the relay will also act as a blossom relay, which will allow you to upload files to your community (and the files are also encrypted and shared in the same way).

I don't think that the space required to download and decrypt the group state is a concern right now, nor is it in scope for Eve to be honest.

The expected use case assumes you communicate with your community from a single device, sharing data from other devices to the one running Eve is a solved problem (syncthing works well for example).