Introvert in MBB?

Short answer (kinda unhelpful): Probably yes, it depends.

Longer answer: I'm at MBB, and although I am in London, I have met >100 people from other offices worldwide (between training and just cross office cases), and frankly, while I have definitely seen a large proportion of "over achievers" and people who just always work hard and go above and beyond, I have met many of them who were definitely closer to the introverted end of the spectrum than to the extroverted end.

My own experience isn't super useful, because I oscillate between both extremes. But I definitely know people who while they enjoy the work and the people in general, prefer to keep to themselves, are more quiet, and tend to keep to themselves more outside of work hours (and even during, to an extent). As far as work is concerned, they'll engage as much as they need to (e.g., engaging with clients, presenting, talking to internal functions), but they might choose to WFH a couple of days a week, or will keep social events at work to a minimum (or just flat out not go). On average, they're just as good as anyone else (as you would expect) and I don't see them having any issues with promotions or staffing. Caveat that this is for Bain, where we don't have to actively seek staffing opportunities as much and networking is less important below M/SM level.