Does using a sub-domain for static resources improve performance even if network latency is introduced?

Does using a sub-domain for static resources improve performance even if
network latency is introduced?

We are working to switch our web infrastructure to use a single sub-domain
for static resources as per Yahoo's web standards advice. This is
theoretically supposed to improve performance because it will allow
browsers to make requests asynchronously to grab the static resources that
are needed. We are using Cloudflare as a CDN and I'm a little bit worried
that the additional latency that will be added with DNS pointing to
Cloudflare's any casted IP range (while only 15ms) may defeat any
performance benefits that would be gained by switching to a static
sub-domain.
I'm still struggling to see why going over the network and making another
HTTP request could be faster in any way than using I/O inside the
web-server to directly reference the static file. Is this really
beneficial?