Yes, it is possible, but you will notice a difference in how you feel initially. I raced while adhering to a vegetarian diet for a season, and found that recovery was much more difficult to achieve. Don't let this discourage you from living a vegetarian lifestyle - there are many health and environmental benefits that come along with it. You will have to take more time in planning out your diet however, and as was stated above, a large portion of this time will come in the form of checking nutrient composition (specifically amino acid profiles) of the foods you eat. Carbohydrates shouldn't be a problem. In general, macronutrient composition in your diet won't actually be that difficult to maintain. You may want to consider a carnitine supplement as an athlete, and if you are vegan, a vitamin D supplement as well.