Working without a connection
kyte reads and writes on your machine, so most of it does not notice the network at all.
What still works
Opening apps, reading lists and records, creating and changing rows, writing documents, running through a process, filling in time — all of it. The app does not grey itself out because a server is unreachable.
What waits
The agent. It needs a model, and unless one runs on your own network the model is reachable only online. Ask anyway and you get an honest error rather than a hang.
Syncing. Your changes queue up and go across when the server is reachable again. You do not have to do anything about it.
Signing in offline
A device that has been signed in before stays signed in: the session is restored from disk and the workspace opens, server or no server. Your first sign-in on a new device needs a connection, because it goes through your Pirol account.
An unreachable server is never treated as a refusal. It cannot lock you out of your own data — see where your data lives.
Coming back
Nothing to press. The app notices the server, sends what it queued, and picks up what changed elsewhere.
If the server has meanwhile been updated and the app has not, it says so instead of syncing rows it does not fully understand: update the app to continue syncing. See version and updates.