It's not the best breed for the job, but it can be done... slowly.
I've volunteered in many CTR and seen draft regularly: belgian cross, percheron, fjord. You have to train very gradually and learn to know your horse: resting pulse and speed of recovering pulse, speed and distance limits. With training, you'll figure if you horse can do it and if he enjoys the job.
Like others have said, it's unlikely that he'd be very competitive, but since that's not what you're looking for, I see no reason why he couldn't do just about any distance you wanted.
As said, he might have trouble finishing the distance in the time allotted, but the distance itself should be no problem.
Granted, my current main saddle horse is only half draft, but he's almost as big as his Belgian momma and has easily covered 15-20 miles in a day, much of it at a long trot or a lope.
Granted, I have no timeframe for the distance because we were moving cattle at the time but still... His long trot is a typical horse's loping speed and his lope is almost as fast as a standard horse's hand gallop.
He was at stud for few years, he was only gelded because his owner started a family and couldn't give him the exercise and focus he needed. He's actually seven years old.
It sounds like as long as we go slowly and take care in the heat, the level i'm looking to do won't be a problem at all.