Cold oil is far more viscous than oil at frying temperature - remember why you usually filter oil for reuse as hot as you can get away with! Unless any seals are built in a way that they take advantage of thermal expansion (unlikely!) to seal tighter at operating temperature, they would fail during operation and not at rest with cold oil.
As mentioned already, oil is indeed a very good electrical insulator - actually, high voltage equipment is routinely filled with oil (not edible oil though) for that reason.
Still, any appliance design that could fail by letting oil into any wiring where it is not supposed to be would be defective safety-wise: While immersion in oil is a good idea for aome electrical circuitry as mentioned, having oil residue and air around wiring that could get hot is a potential fire hazard.
Oil could eventually penetrate plastic (very very slowly), but never metal, glass or non-porous ceramic...