An alternator needs a field current to "excite" the field coils, before it can produce any charge. This needs to be provided by the battery and if it is completely flat, no current might be produced even though the alternator spins as normal. The charge / ignition light on an alternator equipped machine is a critical part of the system - if it doesn't light before start, there is a fault because it shows no "exciting" charge to the field coils - it's connected in series.
Conversely - starting, then flying, an aircraft with an almost flat Ni-Cad battery by other means might not be a good idea because IF the alternator DOES charge, it might cause the battery to overheat due to the very high rate of charge that will result.