It can be played that way, but I and many others find more satisfaction in having one player control two heroes while the other player controls Sauron. This avoids the need to use the special rules for one Hero vs one Sauron player. I never really cared for them that much and it's more fun having two heroes on the board anyway IMO.
After playing a 2p game that way, I'd end up doing the same. Even if the hero gets two turns, it is better to have two heroes. Otherwise that single hero needs to try to run around and cover the entire map.