Sure, this could be built. Do you remember how that light would get brighter and dimmer as you sped up or slowed down? This voltage variation would be the biggest hurdle. You'd probably do well to include a battery that you charge when you're over the target voltage and makes up the difference when you're not. Cell phone battery chargers are expected to have some smarts in them and not damage or overcharge the phone. You'll need electronics and a plan to smooth all of that out.

And when I read it, I was hoping you were planning to power the bike from the cellphone...it sounds like more fun. Maybe someday our cellphones will store enough power to do that.