Does running WordPress on Nginx do “squat” for its performance?

“squat” is synonymous with “nothing” in this case. So, I’d say:

Before you consider using nginx, be aware that PHP APC or a similar
opcode cache with a WordPress caching plugin is going to offer
significant performance improvements over just switching from Apache
to nginx.

If you aren’t already using a PHP opcode cache and WordPress
caching plugin, nginx will do nothing for your WordPress-based
website’s performance.

The way I understand it, these points talk about premature optimization. It says, don’t just move WordPress installation from Apache to Nginx just because everyone says Nginx is a better performant web server than Apache (although it’s probably true).

Try optimizing Apache first, enable opcode caching, try application accelerator like Varnish, etc. Doing so, the setup can offer significant performance improvements over just switching to Nginx.

If it still doesn’t satisfy you (i.e. if the gained performance is still not acceptable), that’s when you should actually consider moving your WordPress installation to Nginx — especially because WordPress has limited support for nginx-based setups as of now.

WordPress is intertwined with the Apache world so support for
nginx-based setups is limited but growing. Factor these things into
your decision to use nginx.