Some alternators ironically require electricity to make electricity. They don't have permanent magnets inside, but instead use electromagnets. So from a stone cold battery, if there's not enough power to get those electromagnets functional, you don't have a way of converting that rotational energy into electricity.

https://en.wikipedia.org/wiki/Alternator#By_excitation

I do wonder how much current that requires, though. In a pinch, could a duct-taped string of AAs be enough to get you going?