The myelin sheath matures from the head down towards the anus. It's possible to be continent but not able to know when you're about to have a bowel movement until it's way too late. So far as social development goes, the child's behavior as described is perfectly normal and age appropriate. Being smart doesn't give one more life experience. You get that by living and by having social experiences.
School CAN wait.
In fact, waiting was the best thing we ever did for our youngest child who matches the described child almost exactly. The answers I've given are the ones we learned the hard way. He's now blooming, teaching himself fractions, division, spelling, and the social graces. We followed the doctor's advice and waited on the formal schooling. Answer Gifted education still does not seem to get the same attention as the education of children with disabilities.