Google has its own pre-fetch both at bot and browser-client level, and there is a high chance it wont run that JS as a bot. Actually it doesnt run most JS unless its from its own Googroot (like conversion, analytics, tagmanager container).
That being said, there are significantly better layers to optimize for pagespeed. Google even has its own Apache module (mod_pagespeed) that can offer significant improvements at server level by processing images, minifying code, consolidating responses, and more. It comes down to pure server response time though...how fast can it respond at first byte? How fast + efficient can it parallel thread? How fast can it rip through big DB queries?
Also, about that hover pre-fetch mod may significantly slow down the web experience for many visitors to your site if they hover for tooltips, right click stuff to save, skim over it while touch, etc...especially mobile or limited guest Wifi. Combined with the similar predictive pre-fetch from Chrome itself, the 2 will stack resulting in even more bandwidth.
In my opinion, this mod is not what it may seem :) Broadband is fast enough, the delay it saves will not be noticeable VS the angst it causes your slower users.
Im not being a negative nancy, just be careful with that :)