First of all: Alexa Rank is not accurate at all, and to answer your question... NO, It won't and not currently used as a ranking factor within Google search engine
Alexa does not affect Google rank. It DOES however provide a few links to your website, which indirectly help, albeit slightly. There are much more productive things to worry about as a webmaster.
It would never affect the SERP. It is not a factor that search engines look at when they show results. They are different and have no link on each other.