Ignoring food safety for a moment referring to an example like How Clothes Dryers Work in most dryers air enters near the top, is heated by an element at the rear of the dryer but the air is actually being drawn in / out by a fan at the bottom of the unit. The internal temperature of the air ends up being about 175C so most of what is "floating around" in the dryer will be steam in normal use.
While the electrical conductivity of pure water is very low the actual conductivity depends on contaminants. Those contaminants will be present inside a dryer but intuitively I'd say at they would be well distributed given the fast air flow. I'm not sure of the conductivity of turkey fat itself but it obviously remains a liquid at 175C and contains many contaminants.
So the real problem I'd see is turkey fat would splatter on the heating element and get within the evacuation fan. Both those events could change their electrical resistance, increase power draw in areas and cause hotspots that could cause a fire. It could also clog up the various vents leading to further overheating.
I guess the answer to that would be completely prevent the possibility of fat / juices escaping during the process. A regular oven bag probably wouldn't be durable enough but maybe a modified pressure cooker vessel of some form would be suitable if you didn't mind a bit of wear and tear on the drum of the dryer.
But getting back to general cooking method I wouldn't see it any different to using an oven to do the same. Results would either go from either dangerous from a food safety point of view to just nasty and overcooked on the outside, especially with something as large as a turkey.