When you're offline, you can view messages. However, only the most recent messages are cached in the account, and caching is run lazily with the background activity scheduler, which won't run if your device is under any kind of load and runs infrequently on battery. Overall, I eventually plan to offer a "days of mail" setting to make this more predictable.

You can also take actions on messages – marking them read, starring them, replying and sending new messages, etc. This is all architected to work while offline and replay when a connection becomes available. This design is necessary to make things seem snappy when the client is online.

Overall, I have not yet heavily tested the offline capabilities, and there is some work to do around the caching predictability story. If offline access is a very firm requirement, I would recommend a client designed around this model, like Mail.