In effect, yes. As you exercise, your aerobic fitness improves, allowing your body to meet the demands of increasingly difficult workouts. These same aerobic adaptations also teach your muscles to repair themselves faster; the fitter you are, the sooner you recover. Unfortunately, if you ramp up training intensity quicker than your body can adapt, you'll override the recovery benefits, requiring a huge dose of rest. The best way to speed recovery time is to increase your training volume over a certain period, commonly three weeks, then slot in a rest week immediately after, giving your body the chance to catch up.
Carbohydrate intake also seems to play an important role. In a recent study reported by the American College of Sports Medicine, subjects were asked to run 16 to 21 kilometers every day for a week and to treat each run as a race. Test subjects experienced decreased recovery rates when they consumed only moderate carbs throughout the week. But when their carb intake increased, their recovery rates were faster and more complete.
While there's no magic bullet for recovery, intelligent training and fueling could mean a little less rest after your next big workout or race.