It was done for a long time on BBSes, and there are sites out there that do it all the time. There are also plenty of PBM games out there, I'm sure. Everyone logs in, makes their moves, and then at a predesignated time (midnight, every hour, every week, whatever) the computer makes all the moves simultaneously.
Considering the amount of MM in Civ, you'd have to do a complete redesign of the game to suit a proper MMO so people wouldn't need to spend hours on a single turn. The MOO3 idea of "Experience", where you're only allowed to do so many things in a given turn, could be crucial, combined with competent AI governors.
OR you could see some players taking the role of governors instead of civ leaders. This has been done in some large wargames to allow multiple people to play. One player may be the overall strategy leader, someone else might control a few cities of the empire, someone else might be the general who directs the overall strategy picture, another could be in charge of a group of units tasked with invading at a certain point, and so on.
It'll require a lot of out-of-the-box thinking to pull it off, I'm sure, but not much of it hasn't already been done in other forms. I can imagine a general trying to get the head general to send him reinforcements, and that guy trying to get the civ's leader to build more military units, and THAT guy trying to get his governors to crank out more units. Anyone can request the use of a unit or city (to control what it does), or can relinquish it. A given person really can't handle the operation of a really large empire, and you'd HAVE TO form teams, each with clear responsibilities, some of which could have overlap, and therefore require the occasional negotiation.
Such a system could EASILY lead to revolts within the empire, as one person refused to do what another wanted, and so one of them uses forces under his control to force them to obey, or forcibly take control away.
Not a complete idea, but a lot of it could work.
