My two cents.....
My son who is 8 has been full grade skipped 4 times to 7th grade. He has been further accelerated to 8th for 2 classes and 10th for another. He gets along really well socially and loves his school. Friends? No, not one child that he considers his friend. Acquintances, schoolmates, but not friends. If he was still in 3rd grade, the results would be the same, he can't connect with his age peers.
That said, he wouldn't change it for anything. He has friends outside of school, a select few that he trusts to take him at face value. Why does a childs social experience have to be relegated to the halls of the school? My son is very social. He gets along well with everyone, he just doesn't consider many people "close friends". He does fine in group projects, he doesn't eat lunch alone and is invited to play Magic with the others.
When you join the work force you don't choose a company or a career based on social aspects, you base it on fit. Getting along in a diverse group is a very important skill, one that will serve him well as an adult. In my mind the "social" argument is an excuse. Coincidentally the same jackass excuse that gets used to dog homeschoolers. Fact is, it's getting harder and harder for schools to justify their actions when all of the studies point squarely at placing children based on ability rather than age.
For your little guy, once testing is complete you will have a snapshot, a better idea of where he needs to be. The Iowa Acceleration Scale will give you a very good idea of whether your child is a good candidate for grade skipping. That is what it is designed for. It takes all of your personal beliefs and baggage, puts them aside and gives you just the facts, ma'am...
Most importantly, and most often dismissed in all of this is the "mommy gut" (or daddy gut). What does your gut say? You know your child better than anyone, what do you think? Don't ever believe that someone with the alphabet strung along behind their name automatically knows whats best. Most of them are biased one way or another, for or against. They don't know your kid, you do.
It's a hell of a ride, trying to raise one of these small people. Trust yourself, let the "Mama" in you ring through and you'll be just fine.
And now, I will climb off my soapbox......