Current from the battery can't change blade power.
Sure it can.
The charging current into the battery represents a load on the shaft. (It magnetizes the coil assembly so it tries to "stick" to the magnets, so they must be pulled apart by power from the turbine. Thus is energy conserved.)
Mechanical power is force times distance moved - which in a rotational setting is torque times RPM.
When it's free-wheeling the only torque felt by the turbine is friction in the genny (bearings, eddy current losses, etc.) RPM is high but torque is almost non-existent. Thus virtually no power.
As the battery loads it up the current goes up, and thus the torque goes up. The blades slow down a bit relative to the free-wheeling speed. But the product still rises. Thus the power goes up. At the blade-air interface the blades are going slower, which makes the angle of the "apparent wind" change, increasing the amount of lift on the blades and thus the torque on the shaft (which comes mainly from the component of the lift vector that lies along the direction of rotation).
Load it up TOO much and the angle of attack becomes great enough that the airstream "detaches" from the back side of the blades. Lift is drastically reduced. This is "stalling". Dropping torque AND dropping speed means REALLY dropping power. Dropping torque with increasing load can produce runaway positive feedback that quickly brings the mill to a near-halt (unless the slowdown reduces the torque again).
This is how stall-regulated turbines work, in lieu of furling. (Though it's a pain to get the design right, and they tend to be very noisy when operating partially stalled, so other furling systems are better for us.) It's also why, once shorting the alternator has brought the blades to a near stop, the alternator no longer produces heavy currents in the wiring and doesn't burn out. (And the high power when the blades AREN'T stalled is why, if your alternator is too weak to pull the spinning blades into stall, you'll fry it TRYING to stop the moving turbine.)
So the battery+load current, by loading the shaft, DOES affect the power produced by the blades. A lot.
