Actually, this would NOT be caught by "black box" testing, since the current date of the iPhone is set automatically. You would specifically have to override the automatic date function to simulate the transition to 2011, then run the alarm test.
The iPhone sets it's clock from the network. You could setup your own mini-network, completely isolated from the outside world and then the network's time servers could be adjusted as necessary. The iPhone still sets the clock on its own and it can be tested.
And setting up a mini cellular network for testing isn't far-fetched. Apple's probably done it, I doubt AT&T or any other carrier (or the FCC for that matter) would allow an early prototype phone on their network