You bet! We just call it "the munchies" (as in: "I'm not in the least hungry, but I've got a serious case of the munchies")
For the most part, it is a short-lived urge that will go away if I get distracted for a few minutes. Other times, it is from choosing a meal or snack that I really didn't find satiating / filling. The food I had might have been flavourful and highly nutritious, but just didn't have the volume / texture / flavour that I needed at the time to feel both full and overall satisfied.
When this is the case, then I find that it is usually volume / crunch that I am looking for. A plateful of veggies with dip, a sliced up apple topped with cinnamon and ginger, or a mix of nuts and fruits all usually do the trick. Other times I'll choose crackers with cheese and pickled vegetables, or a bowl of dry cereal with nuts, or a plateful of leftover roasted veggies with a splash of balsamic vinegar. If it is really wanting "sweet" at the end of a meal, then I have a serving of frozen cherries or berries with Greek yogurt, or a frozen yogurt bar, or a square of dark chocolate, or an occasional bowl of ice cream. I keep whichever choice to measured servings that fit in to my overall plans, and thoroughly enjoy them.
I enjoy food for more than just "fuel" or "nourishment", so figure that honouring the "munchies" by indulging in the right choice to suit the sensory desires of the moment is a reasonable fit in my "healthy enough for me" lifestyle.
Sir Terry Pratchett: "Science is not about building a body of known 'facts'. It is a method for asking awkward questions and subjecting them to a reality-check, thus avoiding the human tendency to believe whatever makes us feel good."
If you have an actual itchy mouth, it could mean allergies. If you are wanting to keep eating and eating and eating, you probably haven't made the best food choices. That is why it's so important to eat nutritionally sound and balanced meals.