Does it matter if a child has a mild form of autism and it not be recognized by his doctor?

Depends: Autism has many levels of severity and presentations; the difference between "mild" forms and normal behaviors such as shyness can be subtle. If the child is functioning fine, then a diagnosis is unlikely to help. However, many doctors are not skilled at diagnosing autism, so one not recognizing it is not proof there is no problem. If you are concerned, find an expert in autism for assessment.

Mild autism: While mild is better than severe, being on the pdd spectrum still places any child at risk for educational and social challenges. Best to get a good, comprehensive evaluation of the child's strengths and weakness and promote the strengths, but provide support for any weaknesses discovered.