Short answer: No
Long Answer: At one time, Turrets used to gain attack damage and attack speed for each allied champion near the tower, but this is no longer the case.
Turrets do gain attack damage as time elapses, and they do gain armor if there are no minions around (this is to discourage backdooring), but these happen regardless of the number of players connected to the game.
Additionally, Turrets lose armor and magic resistance as time elapses. This is to encourage quicker overall games.