Hello Renato,
Your hosting provider could be asked about mod_pagespeed, since it requires manual installation and would only be possible to do if you have root administrator access to the machine. This wouldn't be the case under shared hosting as a website owner. As such, simply contact your hosting provider to ask about this module.
I highly doubt that this module improve
SEO ranking, since the basic purpose is to optimize sites that have been poorly coded. Rather than using a module to improve page coding, it would be better to code the page well in the first place. Here's a description of what it does:
mod_pagespeed Overview
Tests on it for various types of pages were performed and all showed high load times (worse performance) using this module. Nothing on the module page indicates it would improve
SEO in any way either.
Thanks!