Both scenarios are possible but would ultimately depend on the age of the breaker or GFCI outlet and the amount of power being pulled at once. Tripping would most likely occur when the outlet is pulling more power than it can handle, which should never be the case when you’re cooking on an electric apartment grill. (Remember, most models are designed to be the only appliance on a circuit when in use, and failure to do so leads to drastically reduced performance.) So, if an electric grill trips your breakers or GFCI outlets when on a dedicated circuit, that’s generally an indication that the power supply has aged to the point of needing replacement.