The bounce rate supposedly affects PageRank. I'm not sure however if this fix also fixes the bounce rate Google uses internally for calculating PageRank.
AFAIK, PageRank is independent of GoogleAnalytics and does not examine bounce rate (which it cannot know). PageRank obviously works for the majority of webpages that do NOT use Google Analytics for example.
Yes, but google could still use the statistic information to adjust it's pageRank. We don't know. Though it would be easier to trick than the reference counting pageRank algorithm
This is a very interresting news if this is true. I'm managing a web site with one page containing article abstracts and references to pdf files. Our rank is surprinzingly not very good. I will try the proposed change and see if things get better. Articles are original content of scholar quality level.
Why in the world are you surprised the rank is not very good? If the site is one page + links to PDF's, you're unlikely to have a large number of inbound links, which means your pagerank is unlikely to get particularly high.
Indeed, according to http://www.w3schools.com/js/js_timing.asp, the first parameter of setTimeout should be a function. I don't know if "_gaq.push(['_trackEvent', '15_seconds', 'read'])" will be treated as a function.
Your analytics data. Google has repeatedly said that they do not use said information for ranking at all. You should use analytics for insight into you users, that's it. Use it however that best fits your needs.
Also, you should put that code in a function closure rather than calling new Function():