I'm going to bring up a coworker/friend's social awkwardness in an attempt to be constructive towards them.
How will bringing up his awkwardness help you with being constructive?
I don't know, I haven't said anything to him mostly because it's awkward to start it.
Making people feel uncomfortable is not good, and what you're planning may make them uncomfortable and worse, mortified. I would talk with them privately and talk about the issues with them one on one, so that they would feel safer and not feel shameful to others.
The reason I never say anything and the reason the poor guy is awkward is because no one ever likes to talk to him. No one has the initiative to bring him out of his shell. That's why I'm going to take this to the group so that we can learn to be more comfortable with awkward people.
You should find another way to get him to talk more. That plan is going to make everyone involved upset at each other.