Power storage may continue to improve, but it will take a long time before you hit the energy density of fossil fuels; the difference between batteries and fossil fuels is something like a factor of 10 (actually greater than that, but electric motors are more efficient so let's say 10 for the sake of argument), and it's improving much more slowly than Moore's Law, doubling maybe once every 10 years. That means if those trends continue (and there's no guarantee they will), you're looking at 30-40 years before the energy density allows electric helicopters to be competitive with fossil fuel powered.

For cars, energy density isn't quite as important, as the weight of the car is not the dominant factor in its efficiency (it does have an effect, but the aerodynamics, engine efficiency, transmission efficiency, tires, etc. all make a big difference too). But for a helicopter, every pound you add to the batteries is another pound you have to lift, so energy density of your power source is quite important.

So, if trends hold on battery technologies, it will come about eventually; but I would put money more on the decades timeline than the years timeline.