I understand the point you raised, MD. I'll be honest that this is one of those that I really don't know.
I would suggest that you cannot exert him.
The basis I use for this argument is the card
Foes of Mordor appearing in
![Gondor [Gondor]](https://lotrtcgdb.com/forums/Smileys/classic/gondor.png)
Wraith decks. That is legal to exert the
![Gondor [Gondor]](https://lotrtcgdb.com/forums/Smileys/classic/gondor.png)
Wraiths, even if there is no eligible
![Sauron [Sauron]](https://lotrtcgdb.com/forums/Smileys/classic/sauron.png)
minion in play; however, if a
![Sauron [Sauron]](https://lotrtcgdb.com/forums/Smileys/classic/sauron.png)
minion
is in play, you have to wound that minion.
With no
![Sauron [Sauron]](https://lotrtcgdb.com/forums/Smileys/classic/sauron.png)
minion, you are exerting and then carrying out as much of the result as you can. With
Greenleaf, in the same manner, you must carry out as much as you can. I.e., wound a minion.
-wtk