What a sight! I like it

This is, essentially, the same thing as a bike computer (I'm sure the irony was intended). The only significant difference is that the bike wheel is semi-deformable. However, the bike wheel is considerably larger and therefore less affected by small uncertainties in radius, and accordingly, circumference (I'm referring to absolute uncertainy, not relative).

As I mentioned previously, for a typical 700c road wheel you need to compress the wheel by ~3mm for an entire revolution to introduce an error of 1%. If you sit on the bike for the rollout, use road tires, and keep your tires properly inflated, it is hard for me to belive you'd exceed this (e.g from riding position, etc) in a systematic manner.

Sorry for being repetitive, but I feel pretty strongly that even with all the possible sources of error, if used properly, your bike computer will give you a very accurate measurement of the actual distance you ride. This isn't hard to do, and you'll know your milage within 1% (less than one mile on your century).