During an Associations Live Match you will see your players' condition dropping, just as in a usual match. Don't worry--their condition will be restored to the same exact level as before the match, as soon as the match is over. However, keep in mind that your players' starting condition is still important. If you start the match with a tired player, then they will likely not be able to give their best performance.
What's more, your players will not get injured during Associations matches!