There are lots of stories of kids failing socially when they are not with kids with similar emotional intelligence. I know people who have skipped only two grades who are brilliant, but socially off.
It is likely to depend on the child and what they would do well in.
As a fairly clever and socially off person who wasn't allowed to do any kind of accelrated program, I want to ask how sure you the acceleration is the casual factor, rather than say some underlying biological thing?
There are also uncountable stories of people hating school and finding relief upon graduating, and this is plausibly because it's a bizarre environment composed almost exclusively of kids. Personally, if I was gifted enough to go to MIT at age 13, I'd much rather do that than go to a typical middle school, the OP's experience notwithstanding.
I did not have this experience; a commenter upthread did. I was very lucky and had the opportunity to go to a good middle school and highly accelerated high school (Thomas Jefferson HSST in Virginia). But, knowing what I know about normal middle/high schools and MIT dorms, I would have rather gone to the latter than the former if those were my options.
It is likely to depend on the child and what they would do well in.