The short answer is "Yes," but consider a few facts. First, how old is your baby and how is your exhaustion level? If you've been a runner for years prior to having your baby, you'll bounce back quicker than a beginner. However, even if you're newer to running, nothing should be stopping you. In either case, start your postpartum routine out slowly and pick up the pace as you feel yourself getting back into the groove. Don't push too hard at first. You'll know what you can handle within weeks of beginning your training.
Second, your milk supply is an extremely important factor to consider. The goal is to maintain the quality and quantity of your breast milk. During any form of intense exercise, you must superhydrate your body: In other words, drink a lot of water. Also, before a long run, remember that you're burning a lot of calories and need to eat plenty of carbohydrates to sustain your supply. You already need 500 extra calories a day while breastfeeding. But take into consideration that you'll use extreme amounts of energy training for a marathon. So you'll have to increase that by at least another 500.
Good luck with your training. Your body has already been able to withstand an intense journey. This should seem like a piece of cake.