I don't really think it's feasible in normal table-top play for GM to balance both his own character and GMing the game. More to the point, I feel that it steals some of the spotlight away from the players, even if the GM [i]is[/i] being fair about it. 
The only way I've seen this done that I wouldn't mind personally, is when every player is also a GM. And in this particular example case, each person rotated the role of GM every week. So they all contributed as GMs, but were all also players.

In forum roleplays, it's not only feasible, but been done and, depending on the situation, encouraged. Some games have a team of CoGM's, making such an option even more viable.