The reason a severed finger can’t fool the scanner is twofold: the technology relies on both capacitive technology (where the body’s slight electrical current is transmitted to the device) and radio frequency (RF) waves to function. The RF waves are the clincher here: these waves penetrate the outer layer of the skin (and any dirt or scars) to read the living tissue underneath, where your nice clean fingerprint lives. So there’s no chance a chopped-off digit will still work.
Even with a suitably battery-charged finger, any light-fingered thief would then also need to bypass your other security measures, be they a password, PIN- or pattern-lock. I suspect if someone had just relieved you from the ability to count to ten you’d be pretty unwilling to offer up that information, so chances are this added layer of security will remain exactly in the place it was always meant to be. So you can hold on tight to your iPhone, and your fingers.