First of all, the gag reflex is a defense mechanism. It keeps us from eating something based on signals from our sense that the thing is bad.
We learn through time what is bad and we get gag reflexes to foods that we don’t like or have had a bad experience with based on our memories.
My guess, and it’s just a guess, is that the actual defense mechanism can never be suppressed completely, but you might be able to suppress a gag reflex that is based on memory and experience.