Not exactly the same thing, but track racing does quite a bit for my high end, high cadence power. The ability to produce power at 150rpm for minutes at a time isn't something you usually get on a road bike, but it does come in handy at the finish.

Plus just a few hours of track riding/racing and I feel completely whooped the next day, so it must be doing something

As for fixies on the road, I'm not sure there would be as much benefit. And for gods sake, put a brake on it!