Normally this wouldn't be a good play, but let's say that 4 Livre on the bottom of the card was relevant as it could potentially make an extra VP.
Another scenerio: I am almost completely out of Livre and can't afford any of the available actions (or all Musician & Statue spaces are taken). Obviously the only action I'd have available is Depute for 4 Livre.
No. The orange-colored cards are specifically scored only at the end of the game, that is to say, after the left turn of the game.
If you send them away, you no longer have them to score.