I became a stronger rider when I started riding fixed gear. Although, that also could have been because I started riding a lot more about that time.
My credo has always been "when you can't coast, you don't coast, and when you don't coast, you go faster."
What riding fixed does for me is this. When I'm going along and I hit some headwind, or a grade, on a geared bike I just change gears and slow down. But on a fixed gear, I just have to deal. So I learn to focus on the engine a lot more. Concentrate on my spin, my breathing, and relax every muscle I'm not using to power the bike.
That may not make me a stronger rider, but it makes me a better rider.