The solution you have in mind sounds terribly inconvenient, but I can understand wanting to keep the focus on the app.
What would this mean for accessing your service with and iPad or a tablet? I really feel like a traditional log-in system might be better in this case..
For the iPad it's no problem - we have a universal app but you're right - it's not a pretty approach and we have quite a few customers asking. Mostly it's the "desktop bound" ones that want it e.g. the receptionist at the dentist.
