Rapidly varying electric fields inside dust storms have been observed and studied for years. The winds in the strongest Martian storms reach 60 miles per hour.
It is possible to generate electricity from Martian dust storms in the sense that you can get a non-zero amount of energy from it. However, the energy available, particularly from the method you specified, is very little and most definitely not enough to power a colony. On top of that, dust storms are by no means frequent enough to sustain any sort of significant amount of power, even with perfectly efficient batteries. Even on earth, generating electricity from thunderstorms is wildly impractical, without the challenges of trying to do this in space.
Sources and further reading: Wikipedia: Atmosphere of Mars NASA article on electricity withing Martian dust storms
Yes, it is possible. When everything is taken in to account, you can get a modest amount of wind power on Mars. The thicker atmosphere takes away some of the penalty, and the generally higher wind velocities. It could be an important backup power source for when there is no solar power available.
It will follow the traditional wind power model, however, and not somehow using electricity moving through the storm or something like that.