Great question that you ask and timely for me. I actually since last year have been battling Dermatitis Herpetiformis/DH which is a bad skin rash caused by gluten. Here is my experience. I went off of gluten for a full two months and the rash and vicious itching went away. Long story short, YES gluten free is healthier for you if you are INFORMED and are reaching for whole fruits and vegetables, nuts, seeds, lean meats, water, etc.
What ALSO went away were some fine lines on my face, dandruff, a bit of joint stickiness (I am a figure skater so I've beat my joints up more than most people) and I did have more energy. Biopsy and blood tests, came back negative for DH but I was told by doctors and have read that the tests aren't always reliable. I had to go back on gluten to get tested and the DH came roaring back. I simply FEEL better when gluten free, until I had to go back on it to get tested just about 3 weeks ago. Now, I'm back to battling the DH that the tests said I do not have but the doctor said I am a textbook case and all of my experiences and research say so as well. Go figure.
What many people do not realize is that gluten is in EVERYTHING from food, salad dressings, soups and ketchup to mouthwash, hair styling aids, toothpastes, lipsticks and lip balms and these things are what were getting me. I was going crazy because I was suffering from gluten in things that are not even food! BEWARE if you have to be gluten free like me! Gluten can take months or even years to leave some people's systems and their reactions can last that long even if they have been gluten free for weeks, months or years! Celiac/Coeliacs are not the only ones who can truly suffer from gluten, I know from real life experience. Non-Celiac gluten intolerance is real. I've been thinking about writing a hub about my experience but haven't had the time.