I have done a few races (and hope to do a lot more this summer), I was just wondering how many other people here did. I think it is fantastic. The handling, speed, and tight pack situation in a crit is an amazing thing- honestly far more technical and thrilling than alleycats in my opinion.
I would say the thing that riding fixed has helped me the most with is handling skills. I find that I can carry a lot more speed through corners than a lot of cat 4/5s I don't really have the same conditioning as a lot of them, but can make up for it by cornering, and knowing when I can pedal through turns or accellerate out of them. I am kind of the opposite as you, since most of my training is done on my road bike. The fixed gear is mostly ridden for fun and at slower speeds.