Does a GFCI work without a ground? Yes, and they are a tremendous asset for protection of personnel.
An EGC on a GFCI recept can still help avoid a tragic accident, and make them better. It usually takes a combination of events to have something really bad happen.
Let's move to the garage, where there's a GFCI recept in a metal 4S box, an industrial cover, and fed by NM cable. You have an extension cord your friend borrowed, and he ran it over with a furniture dolly a few times, or hit it with his electric weed whacker. There are slight, unnoticed, abrasions in the sheath/insulation. One spot has a very small area of hot conductor exposed, another has a very small area of neutral exposed. Another has a very small area of ground exposed.
You use this cord to plug in the block heater for your truck.
Next time you go to leave, the cord is now laying in a puddle of water from the snow that's melted off the truck the night before. All of the abrasions are in the puddle. How would the GFCI typically perform with/without an EGC?
You pull the cord cap from the truck, and start wrapping it up by hand to get it out of the way. The abrasion with the exposed hot is unknowingly resting in your left palm. Your right hand slides down the wet cord for the next wrap and contacts the spot with the exposed neutral. You're getting hit, HARD. Chances are, a connected EGC would have prevented this.
In commercial/industrial environments, these types of circumstances are not atypical.
If your fridge trips the GFCI, first change out the device. If it trips the new one, fix the fridge. It has a problem that has developed over time. That does happen.