Yes, actually, something bad can come of it--if you don't balance your diet properly after you remove gluten, you're at risk for malnutrition. Not "starvation", but not getting the right nutrients. There's also the risk of getting obsessed with a "perfect diet", to the point of having an eating disorder. More generally, you will spend time and money that you could have spent on something else, and uselessly spend them if you don't need it.
The risks don't mean it's categorically bad. It just means there are risks, like there are to any medical treatment--and yes, diets count as medical treatment. And risks mean you don't automatically say, "Sure, what could it hurt?"
It doesn't work specifically for autism. It is, however, the best treatment for gluten intolerance or allergy. (Intolerance = "cannot digest"; allergy = "body thinks it's a pathogen".) If you are autistic and you happen to have either intolerance or allergy, you may indeed see an improvement in how well you cope with the world--probably because the physical discomfort of your allergy or intolerance is no longer present and you are freeing up more resources than you had before.
Eating "gluten-free" often requires home-cooking food, which is often a great deal healthier than pre-packaged food; you may get a benefit from that. But you wouldn't need to exclude gluten to eat healthier.
Most research has been coming up with the same thing, basically: Autism itself doesn't respond to a gluten-free diet; but autistic people who have problems eating gluten tend to benefit from eliminating it, just like NTs who have problems eating gluten would benefit. They can benefit more than NTs do because they are coping more narrowly than NTs are; but if they weren't gluten-intolerant or allergic to begin with, there wouldn't be any improvement.
I was on GF/CF as a child. I experienced no changes except, perhaps, a relatively short adult height due to low calcium (and a tendency to scarf good-tasting food whenever I could get it, probably a factor in my current obesity). My mother, who has celiac disease, became a great deal healthier when she eliminated gluten. If you have celiac, for goodness sakes, don't eat wheat; you'll rip up your intestine! But if you don't, it's useless bother to eliminate it--better results if you work on an overall healthier diet instead.