I'm only guessing since it's been a while since I've done analog electronics, but my guess would be there is just enough current to move the servo to the correct position.
I could be completely wrong, so take this with a grain of salt (maybe half a grain). If you apply ohms law (V=IR) to it to get current, you get 5V with 80 Ohms which theoretically produces 625mA. But there are a lot of varibles to that. Especially since capacitors aren't ohmic.
It's probably safest to try his route (in terms of circuitry) and see what happens. Mean while... I think I'm going to find my textbook again to study.