Well I suppose I could write at length here.
Its not the autism that is at issue, rather does the child with Autism also have an intolerance to gluten?
If so, then yes, a gluten free diet is appropriate but Autism is a complex and wide-ranging condition and applying broad rules is entirely a mistake.
Each person with autism needs (like everyone else) to be treated as an individual - so you seek to meet their needs.
We have found (for example) that because our son does not like the texture of meat we have to provide him with an additional iron supplement. We noticed improvements in behaviour when his levels of iron intake are about normal.
This is not unexpected and similar results can be seen in children who are not autistic, but have a low intake of iron - in this case it was the low intake of iron affecting the behaviour rather than the autism.
What complicates this is that the less appropriate behaviours are typical autistic behaviours (meltdowns etc.) and are sparked by the fact that his sensory dislikes that prevent him from eating meet are also a result of autism.
I guess what I am getting at is that in our case, the behaviour is the result of iron deficiency. Autism prevents our son getting iron in the usual way that kids get it - our work-around is to supplement the iron.
You need to determine in your case whether or not Gluten can affect behaviour - i.e is this a nutrition problem?
Id be interested to hear more of the circumstances. As well as having a child with Autism I also work in the disability sector.