You could easily/quickly implement this feature using one of the PaaS (Platform as a Service) providers out there. Parse, StackMob, Azure, etc. They provide the database in the cloud and the REST API to access it, and you simply make a read on the password table to see if the entry exists (using the provider API). These services are very inexpensive and you could use the free tier until you get meaningful volume.
However, note my previous comment, that this would not be approved as an app for violating the App Store Guidelines.
Apps that arbitrarily restrict which users may use the App, such as by location or carrier, may be rejected
Apps that unlock or enable additional features or functionality with mechanisms other than the App Store will be rejected