Turns out the registration webpage asks for both your Marriott and UA number. So the only way I can see this working is if somehow they track the stays credited to your Marriott account and then post extra miles to your UA account, outside of the regular posting channel.
But I don't see a way to '"set your preference to UA miles" in your Marriott account and still earn points for stays. Anyway, if it worked out properly, it would be a nice little bonus.