One suggestion I would make: Once your things are set up, you shouldn't have to go to the settings screen to log in. Maybe there could be an 'account' button on the main screen or on the buddy list and from there you could sign in and out directly. I think that would make it more friendly to non-techies.
I'm with moxie. There are already plenty of good encryption apps out there. That 100,000 could have gone to existing apps that do what they say they do rather than an app that might not turn out as promised.
But you can appreciate that as part of risk assessment some people might have a valid reason to be concerned about leaking even that much information?
GCHQ / NSA are good at finding patterns in data, so a collection of "You have $n new messages!" notifications can provide insight into the organization of a group.
I propose it as an option, not a default.
[1] - http://threema.ch/en/
Update: I installed ChatSecure on my iPad and it's very easy to set up. So easy in fact that I'm thinking there must be something wrong with it, because otherwise it would probably be recommended more often in these types of threads...
One of the things that seems problematic is that the background session expires after a few minutes, so if someone tries to just randomly message you, chances are you won't be logged in, so this can't be a replacement for IM.