Could food be used as heating element? Could we heat food by flowing electricity through it as a heating element?
 A: The technical answer is probably yes. Food, like most materials, has a resistance and therefore is subject to Joule heating. This means you can pass a current through it and it will dissipate some power as heat, doing what you requested. 
The practical answer is almost certainly no, however. Think about what this would require: some sort of mechanism to provide uniform contact to ends of a material with non-uniform dimensions, non-uniform resistivity, etc. These factors make this heating method quite impractical — which is not appealing when there are several efficient, cheap, simple solutions to heating food. 
The closest thing to what you describe (in the sense of causing heating in the material itself) in practice is probably dielectric heating, which uses a quickly-alternating electric field to cause reorientation of dipoles in a dielectric material. This increases the kinetic energy of the dipoles, thereby increasing the temperature of the material. This is how microwave ovens work. 
A: 120 VAC electrocution-style hot dog cookers were sold commercially in the US during the late 1960s. I built one as an undergrad physics lab project in 1971. The prongs used to stick the hot dogs have to be made of stainless steel. They are fast, but leave the hot dog ends somewhat scorched. I got a passing grade in the lab, but none of my classmates were willing to sample the result when I demonstrated the device at the end of the term. 
