Can I do it if I have a means to unexhaust?

Are there any exceptions if not?

No, each character is considered either committed or not committed to the quest. Once a character has been committed, even if he later becomes ready, he is still considered to have committed to the quest until the end of the quest phase. So he cannot commit to the quest twice in the same quest phase. Besides, as per the FAQ, all characters of a player are committed to the quest simultaneously; therefore, you can't commit a character, then take an action (or response) to ready him and commit it again.

Mmmm my game balance sense was right. Thank you for being so clear.