A half charged battery would be a huge improvement.
You can get power below 12V and all the way down to very low voltage if you use a stepup regulator. This device stores energy in an inductor by allowing output of the machine to ramp up current in the inductor, that current is interrupted by switching off the control transistor and the inductor discharges into the battery .. the voltage rises to the value that it takes to continue current flow and transmitt the stored energy to the circuit. This is similar to an ignition system.
The advantage to such a system is that it can be designed to precisely transfer the available power for any useful wind speed .... say 5 watts and up, regardless of generator terminal voltage. If wind speed is high and power is not needed the switching transistor can turn on and short the generator through the inductor ... preventing overspeed while "kicking" every few hundred milliseconds to maintain float voltage. One helpful accessory might be an angle of attack vane located between, or at the end of, one of the blades (a dummy would be added opposite for balance). At low loads the angle of attack would be low and as load increased the angle would increase until a stall point was reached. The controller would maintain an AOA a couple of degrees under stall and force maximum generation.
Some people may want to use a wind turbine at a vacation cabin. A situation could occur where there was a breeze all week, the turbine was putting out 6 to 8 volts with the battery at 11.2V .. but no charging took place. If the system had been matched the battery might be fully charged and floating at 14.2 ! The cost per KWH of wind power is relatively high and a transition to home installations might be expedited if you can recover every potential KWH.