Will social anxiety stop one from succeeding in PE/IB?

Incoming analyst at a Tier-2 BB here. I wanted to explore a potential opportunity to start direct in PE, so I have been interning at a MM PE place over my senior year. Yesterday, my VP took me aside and told me that there might be an offer on the table because I am been the best intern that they've had, but they told me they are not sure if I'm cut out for this because social skills aren't my strong suite and they require analysts to also network frequently for deals. For context, I suffer from chronic depression and anxiety (sometimes visible on my face), and frankly I think I only got converted at my BB because of COVID + my colleagues didn't interact with me in-person and I had more control over my facial expression on Zoom calls (because I could see my own video).

I've been trying to address my anxiety issues since freshman year by seeking medical help, attending therapies, and getting out of my comfort zone by networking aggressively. I'm proud to say that I've come a long way, but I am not and probably will never be as smooth as my fellow peers who can charm and connect with people effortlessly.

Just wanted to ask if it's possible to succeed in PE/IB even with severe social anxiety and if anyone has any constructive advise to offer. Thanks!