The HTTPRL module doesn't increase Boost performance, per se. It is a requirement for the Boost Crawler submodule. The crawler module ensures all pages are actively cached; it goes through all site content and requests all its pages so that Boost stores them in its cache.
The HTTPRL module is used here to speed up the background crawler requests; it doesn't need to wait for a HTTP response to get the main Boost module to store things in its cache. The performance boost comes from having all your site content cached so that no anonymous user doesn't take cache hit (i.e. they have wait for the site to build the cache since it's not ready).