Yes, it's possible, though it may be tricky.
You can have a maximum of 18 civilizations (not including the barbarians) in the game at one time, which is important to keep in mind. It's also not possible to add new civilizations to the game once it has started so everyone in the game will have to be part of it when the game begins.
Those two issues in particular make it difficult to do, but it's certainly do-able.