It depends. If he is an ultra low durability C, he may need full rest for his energy to improve. Also, C's seem to tire more quickly when playing C. I had the same player whom had the same durability season over season, but he fatigued a lot more when he played more innings at the C position than when he played DH or RF.
The way that I think aboUT durability is the percentage of games a player can play without getting fatigued. There are 162 games (1450 innings) per season. If the player has 100 durability, he should be able to play all season and some pre season without getting fatigued. I had a 100 durability player that batted leadoff and could overplay COF and 1b. He played every day with no rest and no substitutions, pinch hitting or pinch running. He also played 5 games during pre season and every playoff game on a championship squad and he never got fatigued. However, if that same 100 durability player was a C and I played him at C, he likely would have has some fatigue during the season.