Ryan,
All of the rules run in-browser, so yes, it would return the code client-side. However, I would ask you to reconsider the idea that it would be bad for performance. If you use our default option of non-sequential HTML/Javascript to inject the tag, then it will run in parallel with the rest of the page and will not cause any slowdown whatsoever in the page load or user experience.
Regarding cookies, since the code is running on your website, the cookie will be set on your domain when the rule is run.
Best,
Shawn