When training on a geard bike, you are supposed to look for your "sweet spot" where you are right on the dividing line between aerobic and anaerobic excercize. Shifters and effort modulation are supposed to keep you there.

On a fix, you have to mash crazy up hills, and spin wildly down them. Thus, I would imagine that riding a fix is similar to a workout where you lift your maximum weight for a few reps, jog a bit, then sprint, then lift your max weight again. Not sure how good this would be for training.