I'm not familiar with FreshRSS, but assuming that there's something in the protocol that lets a reader push up a "read" bit on an per article basis

this page references a "GReader" API

I'd assume that that'd depend on the client, not the server.

If the client attempts an update and fails and that causes it to not retry again later, then I imagine that it wouldn't work. If it does retry until it sets the bit, I'd imagine that it does work. The FreshRSS server can't really be a factor, because it won't know whether the client has tried to talk to it when it's off.

EDIT: Some of the clients in the table on the page I linked to say that they "work offline", so I assume that the developers at least have some level of disconnected operation in mind.

The RSS readers I've always used are strictly pull. They don't set bits on the server, and any "read" flag lives only on the client.