As an introvert who works and has worked in an extrovert's role for nearly 10 years now, I'd advise not getting too caught up worrying over the distinction, and definitely don't buy into the stereotypes of either position.
Just like not every extrovert is immediately likable, not every introvert is a smart and hard worker. I know you wrote "may", but I've just seen too many colleagues and too many of my employees fall into this trapping mindset, which can result in some really nasty work atmostpheres. The attitude one brings to a job should be appropriate for the work. There is truth that if you don't speak up, it's hard to hear you sometimes, but that doesn't mean the way you sell yourself is most important - you still need substance.
I've watched as social charmers worked their way into my previous places of employment only to get shitcanned months later when it turns out you have to beat them with a stick to do even the simplest of tasks. I've also seen the same types of people and categorized them the same way, only to find out later that they were really doing tons of great things I just never knew about.
This is more the manager/supervisor in me not wanting people to draw lines in the sand unnecessarily, but who you are is how you want to present yourself. I'm a shy guy by nature, and I know that at my last job my coworkers could never understand why I liked lunch alone or rarely went to company events, didn't buy into company pride, etc. But once I dug in and made an impact work-wise, it was made pretty clear that they couldn't imagine not having me around, even if I was quiet.