You can, and there is a legitimate use for it: I've done it before in my Gollum deck in expanded. Gandalf is a lot easier to exhaust than he is to kill, so play it on him, and drop
Desert Lord and Gollum with Saruman from set 4. Using
Desert Lord and
Promise Keeping in conjunction with the Gollum wounding conditions, you can exhaust Gandalf even if he doesn't fight.
Desert Lord will likely be killed: he exhausted himself in the archery phase. Then remove Gollum from play with
Web, and Saruman is the only minion left, so you can discard the staff to return him to your hand, but most notably, you kill Gandalf in the process.
Tough to pull off, but the Saruman is useful anyway at hitting huge conditions like
Stewards' Legacy, so your only adding one staff to a deck that can discard cards anyway. And if a Gandalf deck losses Gandalf, it's normally game over.