Yes...it certainly does...but it seems to have a low probability. I usually try and have 3 or 4 archer units firing at one key target and then switch if and when they are successfull.

Also I find it a bit off-putting that there is no damage meter monitoring your progress towards success. As far as I can tell one minute the target is 0% damage and safe, the next it bursts into flames and only then does the damage meter start running. But by then the job is done, as there is no way I know to put out the flames, so as soon as you see flames switch to the next target. But watch out for intervening walls, when the tower or ram gets close most archers can't land flaming arrows on it. Thats why on some castles the gates are set back into alcoves, so you can post archers on the side walls and still fire into the attackers.