My twin sons (15) both have NVLD. They've never had the anxiety in social situations/crowds that you seem to describe. But that doesn't rule it out for your son, of course. My boys tend to be pretty upbeat and friendly...then, if you point out to them that something they did hurt someone's feelings or that a person they think is their friend is actually making fun of them, you get a deer-in-the-headlights look ("What?!?! How can you tell that?") Long before I knew what NVLD was, I found myself talking them through non-verbal cues, almost like translating a foreign language: "Try to remember the look on so-and-so's face, just a minute ago. She wasn't smiling anymore. Her eyebrows went up. And she started looking away from you. That means, 'I've lost interest in what you're talking about.' Even though you'd like to say more about the Titanic, it's was time to stop telling HER about it and find a new subject." In other words, my sons seem unaware that they have a deficiency in reading unspoken cues. But I suppose a child who DID realize, "Everyone else is speaking some 2nd language that I don't even hear!", might prefer to avoid social situations. That makes sense.
The difficulty is, more than one thing can lead to a kid not fitting in/not responding appropriately to social situations. If you're sure it's an inability to read nonverbal cues, you're on the right track, looking at NVLD. But an important way to verify that will be looking at his math skills - and that will take time. At the kindergarten level, math is completely verbal (learning to recite the numbers in order and remembering basic number sentences, 5+5=10). So NVLD kids do as well as anyone. Even when you get into learning multiplication and division tables...that's supposed to be a non-verbal skill, as you make associations in your head (Oh, cool! If 3 groups of 5 is 15, 6 groups of 5 must be the same thing as 15x2!). But you can still learn those tables as rote memorization of verbal facts. The more kids range into math that has to be done in their heads and where they have to conceptualize things, before they can even figure out what they need to put down and work out, on paper...the harder math gets, for NVLD kids and the bigger the disparity between their math and verbal skills. But the higher a kid's innate intelligence, the longer it may take for this to show up (i.e., the longer he may be able to continue approaching math as a verbal skill).
Just be patient. If you need a diagnosis so he can get services (a social skills group sounds great, for him!), discuss the verbage options with the powers that be. If it's obvious that he has social issues, there must be some label he can receive, so he gets what he needs. Remember, it's in the school system's best interest that he "be all he can be", as well as his own! But if you feel certain he has NVLD, you can still verbally coach him through how to read non-verbal cues, even if he doesn't get a correct diagnosis until he's older. I'm not saying you'll "cure" him. But verbal coaching - over and over and over again - does help, slowly.