Yup, you're wrong.
If your battery is stone cold dead, there is no power to fire the electronic ignition. No power, no sprk (or glow plug for a diesel).
And if your battery is almost dead and below 10 volts DC (IIRC) your alternator won't charge even if you do get the car running. The alternator needs to "see" a certain amount of elelctrical curtent before it can start "alternating" and producing elelctrical current. The old direct current generator (not around since the fifties) would produce electricity completely on its own and how much was dependent on it's speed.
However, in real world conditions where your battery is just dead enough to click-click the starter relay but not turn over the engine... a push start with a manual transmission will most likely start the car.