Of course condition plays a role, it's one of the few things that actually makes sense in the game, also morale. I don't fully understand your question but If you chose to play hard pressing and man to man your players condition will drain faster during the game. Plus some players get tired faster than others based on their fitness or strength, so you should keep that in mind. Low condition can mean your players will not perform at their best and there is a higher chance of injury. The association players are constantly tired because they are used by their owner. If you need them you need to use your green packs.