A car WILL NOT <i>start</i> without the battery connected - no chance, none, zip, nada. The ignition circuit and starter motor need it. There is absolutely 0 chance the car could ever start from the key without it connected. (It will bump start however, from a push or tow)
It WILL <i>run</i> without the battery connected (or flat) - the alternator (spun from engine) provides enough for the spark plus (petrol engine) and other electrical ancillaries (fuel pump etc.) that the engine requires for it to function. (that's what happens from a bump, or tow, start - the moving car spins the engine and the spinning alternator provides power for fuel pump/spark etc.)