Thanks for the heads up on this thread.Yes, all of WordPress ( including s2Member ), works on cookie-based authentication. That is, a User logs into the site, and remains logged in until cookie authentication expires. So as long as your application can work offline, you shouldn't have a problem recognizing the User as being logged-in, because cookies are stored on the client-side browser. Just be sure they click the "Remember Me" box when they log in, so that cookies remain in existence, even after the browser session is finished.
Cookie authentication in WordPress is handled by this core framework function:
http://codex.wordpress.org/Function_Ref ... uth_cookieFor better security, you might consider a JavaScript version of this routine, or at least something that checks the overall validity of the authentication cookie set by WordPress. I'm not sure you'll ever get something that's "as secure" as a server-side validity check, but I'm sure you could come up with a workaround for an offline app that would suffice.