The short answer is "it's possible." When you file for divorce in the state of Georgia, one of the first questions is what is the date of separation. The myth is that separation means you have to be living in separate physical locations. That is not the case. You can not only live in the same house, but you can sleep (emphasis added to sleep) in the same bed and still be separated. There is a catch: You have to be living in a bona fide state of separation. What is bona fide state of separation? It means no hanky panky: No sex with your spouse. The judge may dismiss your case if you continue to have sexual relations with each other.
If you are serious about getting a divorce, then you should set some clear boundaries (even if you are still sleeping in the same bed).