Car alternators require some excitation voltage to the rotor windings to get started at low speed. If the battery is completely dead the rotor won’t get this voltage and the alternator will likely not produce enough current to power up the car’s systems essential to running. I say likely because residual magnetism probably won’t be enough at the speeds you’ll be able to get the engine/alternator up to by pushing.
There is hope though, if you happen to have a couple of 6V lantern batteries floating around in the boot.
A couple of these connected in series to make 12V, connected with the correct polarity to your car’s battery, will provide enough current to wake up the alternator and get you on your way. Just don’t forget to disconnect them once it’s started - they don’t like being charged and especially not at the output current modern alternators are capable of.