GFCI and Refrigerator and Circuit Breaker
A refrigerator does not have to be on a dedicated circuit, it's simply a convention some builders/Electricians follow.

A ground-fault circuit interrupter (GFCI) trips in response to a ground-fault.  While a standard circuit breaker trips in response to overloads, and overcurrents.

If the combined current drawn of the refrigerator,  mixer, and whatever else was connected, is greater than the breaker rating (for long enough). Then the breaker would trip, but the GFCI would not.

If there was a ground-fault. The GFCI would trip, but not the breaker.  

They are two different types of devices, designed to provide different types of protection.