There has been a lot of confusion about these, so I thought I'd explain them again.
Exhibition games do not affect your team or players on your team. Your player fatigue, injuries, and suspensions do not affect their play in exhibition games. In fact, you can have a player with a broken leg and he can play in an exhibition game. Exhibition games take place outside of the real fake world. What they provide are a means to play against your friends or other teams that are not in your league or world, get more data on how your players play, try out new formations or starters without messing up your league games, etc.
Exhibition games DO NOT affect your club or players in any way. Players will not fatigue from playing games. They won't get injured. They won't get additional development. Your club is not affected by your exhibition performance or the number of exhibition games you play.
Exhibition games are simply a way for you to get more games in, if you desire, and a way for clubs to do something before they are entered into a league.
Hope this helps set the record straight.