Oh hell yeah. There are two major situations where introverts are actually more socially comfortable and extroverts experience anxiety. Often crippling.

1. When there is an insufficient number of people they already know well and like relative to strangers.

2. Online.

Extroverts draw energy from interpersonal interaction, but primarily from their "tribe" and from strangers only when supported by their tribe members and taking on strangers in smaller groups than their own.

So at a party when you have 4 friends from your tribe and there are 20 other people of whom 17 are from another tribe and 3 are solo, your tribe will mostly stick to itself, take on the solos, or people from the larger tribe who can be separated from the herd.

If this is not possible, the extrovert will feel anxiety. I have watched extroverts squirm and freeze in such situations. If an extrovert is flying solo, apart from home tribe, they will often make clumsy, blustering overtures to connect (sign: they'll act like they already know you intimately instead of making graceful get-to know-you moves, triggering a "err...I don't know you" reaction) and get stressed out when strangers reject their overtures.

Online it is a different matter, since relationships have to form via very narrow media first, like text, before you can meet the "whole person" if at all. My anecdotal experience is that extroverts are disproportionately likely to lurk online or try way too hard to move the action offline.