Is it possible to engineer a plant that could grow off of your body (and not fungus, I mean a leafy plant)?

I doubt it. Plants tend to be very rigid and grow their roots by spreading the surrounding medium. A plant-animal hybrid would be very uncomfortable for both organisms: either the plant would break due to the animal's movements, or the roots would tear up the animal's insides.

yes it is possible, but i can't imagine why you would want to do this.

if any species is exclusively dependent on another for it's survival without contributing anything back to that dependent, the organism is called 'Parasitic' (e.g. tapeworms)

if two species are interdependent on each other, gaining mutual benefit from their interdependence, those species are called 'symbiotic'. (e.g. Lichen)

several other species are known to have symbiotic relations, (such as nurse sharks), but no symbiotic relationship has yet been discovered among more than two species. this may be for the same reason that the Bose model only works for the hydrogen atom.

but for a nice science fiction story, yes, your idea would work. good science fiction is based on good science.