Can one cook a duck on a rotisserie?
Will the fat dripping from a whole duck create a problem by starting flames?
Are you roasting indoors or outdoors? If you are doing this outdoors, put a pan under the rotating duck to catch the fat. I don't know what to tell if you are doing this indoors. I would not chance burning the house down.
A duck on a spit certainly can be done in an oven, though have water in the pan underneath and discharge/refill as you go. You'd probably want to run the self-clean afterwards though.
Outside, you must have a drip fan or else you will at some point have a fire.
Certainly you can do it (outdoors with a drip pan), but its probably not going to be a great result. Rotisserie birds sort of self baste -- the surface tension of the rendered fat keeps in on the skin as the bird rotates -- which makes for a soft (soggy) skin. OK with a chicken, but for a duck i'd suspect it would come out pretty flabby, when the best part of roast duck is the crispy skin & rendered crackings. I roast outdoors using medium indirect heat (and a drip pan) to render most of the fat, then fuel up the fire and blast it (indirectly) to get the skin crisp.