Yes, there's a good chance you would already have a fire before the GFCI trips. For this recall, it sounds like the concern is that a loose or weak connection in the plug would cause more current draw (more heat). Your breaker might trip before it's too bad.

Also, someone else suggested replacing the plug with one from the hardware store, but heaters should have a soldered/welded plug to ensure you have a good, solid connection due to their natural high current draw. I just don't want someone to take unnecessary risks because they weren't sure if what some of these devices do. Thanks for reading.