If one head were not online, I don't think its hit points would be added to the hit point pool at all. Thus, the two-headed ogre would simply be a one-headed ogre with a large growth on its shoulder (and one paralyzed arm and a limp). It should play very similar to any other one-headed character.

Also, innovations are not perfect. There would be problems, and that is why they would have possibly changed the pairing system.

There could have been an option to go with a random partner or to input a code that you and another person think up to insure you are paired with that person.

Or, there could be a menu to input when a person generally plays, what time zone they are in, etc.

There are many ways to fix the problems associated with the sharing of a character by two people. The absolute worst way to fix them is to scrap the idea. The two-headed ogre can and should be implemented. Creativity is what keeps games fresh. This would have given WoW a huge advantage over EQ2, but... well...

What is it they say about silence being golden?