With some species it could certainly be beneficial, especially if they're destined for repatriation. Don't think the dog would need a costume - just a plain old dog would most likely be enough. It'd have to be done with some caution for the well being of all involved - maybe start tentatively and see how things go - but it could be a very good idea.
I wonder if it could work both ways - Auckland Zoo's cheetahs are often taken for walks around the zoo on leads. Strolling them through a herd of something could be very enriching for both species, although I wonder if their good behaviour while leashed would continue if suddenly surrounded by moving prey...