Assuming access to the UDID – and absolutely nothing else – is... dumb. What happens when users change devices, for example? I'm having a hard time imagining any large number of apps that are that reliant on this one thing. Even OpenFeint had provisions to handle non-UDID-based account authentication.
No, it won't. This is a deprecation. The API will still be there, and it will still work. Using the API will now have a compile-time warning that developers will see.
At some point — far off, in the future — the API might be removed. But, keep in mind: there are APIs that were deprecated in iOS 3 that Apple still keeps around for compatibility purposes.