Don't you see a progress bar (after clicking the big button to end the command phase) as the replay is generated, I'm not currently the player generating the replay in any of my games but I seem to recall seeing the progress bar in earlier games.
The person that creates the game is the one that sees the replay first I believe, this stays constant througout the game.
Process goes:
Player 1 - Select game, enter password.
Player 2 - Enter password
Player 1 - Place units and give first turn orders
Player 2 - Place units and give first turn orders, generate first turn replay
Player 1 - Watch first turn replay, give second turn orders
Player 2 - Watch first turn replay, give second turn orders, generate second turn replay
And so on.