Is exactly what I did to won my last 5 champions leagues, leave the cup... and tank 2 seasons and play for the league 2 seasons... ...7 seasons = 5 Champions leagues... but remember, that, the player skills have some penaties, for example, for wrong position, less morale and condition.
So, I too have to say that perfectly you can score with a player at "0" condition because the game don't put a penalty under the player like an injurie. With an injurie, the player don't appear, but without condition, yeah.
Of course it increases % of injuerie... but not always is = injurie, like the training. I can train all my team 30% hard 5 times consecutive without injurie.