Conan could handle individual opponents without trouble, but he was often on the run in his early days, fleeing cities just one step ahead of the authorities. He certainly got knocked unconscious on a recurring basis, and locked up more than a few times. Until he joins a faction or starts his own, he wouldn't have a major impact. If he is starting in King's Landing, I could see him going in so many directions. Maybe getting recruited by the Lannisters and then leaving in disgust during Joffrey's reign. Joining up with Beric Dondarrion's brotherhood. Or heading across the sea to the eastern lands. Or maybe becoming a freebooter of Pyke. Or getting shipped off to the Wall and escaping along the way. So many possibilities.