Medieval iconography isn’t my specialty (there are myriad sub-specialties under the rubric of medieval studies), but my understanding is the protruding tongue represents the devouring nature of a demon.
That’s not a theory I’ve ever encountered. Where did you hear that one? A problem with it is that, although as I said the Devil was often shown with a protruding tongue, the vast majority of tongue-sticking figures in Romanesque church art are clearly not devils.
This is my completely wild guess, but the protruding tongue may also have served a practical purpose. Since many gargoyles were gutter spouts, the tongue may have helped contain and direct the flow of water.
Actually anthropomorphic gargoyles with protruding tongues are quite rare, certainly compared to the numbers of tongue-sticking figures on corbels, column capitals, roof bosses, etc., and when they do occur the tongue generally is simply the water-spout. Gargoyles in animal form do indeed often have lolling tongues; but then real dogs’ and lions’ tongues do tend to loll when they open their mouths wide, so I don’t think any significance can be placed on this.