There are many other aspects that are related to page speed that can solve different problems. If your problem is high latency using a CDN might be more helpful. Expires or a Cache-Control Header is good for content that doesn't change often.
Only a little, I'd test it or only have it be one of many steps as I'd think the impact would be minimal. The idea is that the cookie will be sent for every request even though it's unnecessary for static content. Check out this document.
It may or may not help speed up your site. That's going to depend on a lot of factors.
However, it does open up a lot more flexibility for improving your performance. For instance, serving static data from another domain allows you to turn off cookies for that domain. It also allows you to trim other headers. It allows very generous site-wide cache expiration values. Etc, etc.
So while simply flipping the serve-from-subdomain bit will not necessarily offer a performance boost, it does open the door for some significant wins.