Yes, its possible ! But the procedures of having the same game running with the same stage of a game on multiple devices, are different but almost identical.

e.g. - you can play war inc or Prime world Defenders II on two smartphones with the same stage of the game. on 1st case u have the option of recovery account at the very beginning but for the 2nd game u can get that option after completing stage 8 {synchrinize by logging into facebook ac with the user name provided in the player's profile in the game}
So the idea is same for other games too.