He did, when he disarmed him on the tower.
The point was about having to win a duel to win the Elder Wand. Malfoy and Dumbledore didn't fight a duel; and neither did Malfoy and Harry. It was enough, in Harry's case anyway, simply to grab the other wizard's wand to become its master.
I think that the Elder Wand was not "won" simply by who happened to take it; and therefore, I don't think that the wand would have done anything special for Draco Malfoy.
There's a loose end there, by the way. I didn't check in HBP for the specifics, but I don't see how Dumbledore's wand actually ended up in his tomb. If Malfoy lost the wand, and Voldemort ended up with it, then I think Voldemort would still be its "master" if mere ownership was enough.
But Voldemort wasn't its master, because the wand didn't choose him. It chose Harry, though. And I think that choosing was done on the basis of the "Third Brother," who did not try to cheat death. Voldemort tried to cheat death. Malfoy, a coward, did as well. But Harry didn't cheat death, and so became its "master."
In a Scriptural sense, it brings to mind Matthew 25:29, For to everyone who has will more be given, and he will have an abundance. But from the one who has not, even what he has will be taken away.