That sounds more reasonable to me than holding him back on the off-chance that he may fail.
If your son starts cruising towards failure, you can always ask for a time-out and a re-assessment of the plan.
I’m wondering how you will gauge success. If he does well academically and suffers socially in the 3rd grade, will that constitute failure? If you hold him back and he continues to flounder socially, will you view that as proof of his immaturity, confirmation that you made the right decision? Or will you decide it’s not worth it and put him in the 3rd grade halfway into the experiment, if that’s even possible?
It sounds to me you’re risking limiting his intellectual growth in favor of his social skills. As a relatively smart person who is no Miss Congeniality, I have to say I don’t think that’s a good idea. When you’re challenged emotionally/socially, your intellect is the basis of your self-esteem. Being able to say to the bullying/teasing crowd, “Well, at least I’m SMART!” is the only thing you’ve got in your pocket. His classmates won’t see him as the smartest kid in the class, even if that’s who he is. They’ll see him as the weirdo who’s repeating the second grade. They won’t know why he was held back. All they will know is that he is a flunky. In a kid’s mind, smart flunkies do not exist.
If he’s dealing with all the problems you believe he has, then chances are he’s always going to be behind socially. There are a lot of us out there, the socially inepts. I would continue to nurture his intellect and not rely so heavily on the school system to help him with the emotional/social stuff. They are always going to fall short in this department, no matter what they do. But they will be able to make him feel smart.