Yes. Player rest replacements are based off the player rest hierarchy in the Manager's Office. When a player is below his AutoRest fatigue level entering a game or if the managerial settings for resting players during a game have been met, the Sim Manager will look at the player rest hierarchy to see if there is a player available at the position of the person being replaced. It will then take the first available player on the list and insert them into the game. For example, if #1 is available, that player will be inserted into the game. If he isn't but #2 is, the second player will be inserted into the game. And so on, and so on. If an injury or ejection occurs and nobody is available on the player rest hierarchy then it will check the bench for somebody available to come in.
You can also control whether individual players are allowed to be rested by checking the Allow Rest box in their Advanced Hitting Settings.