main use of Alexa search engine is to check how much your site is popular in the internet. means your site daily unique visitor and also your site total monthly visit.

In my own point of view, it does not help anything, well everyone know about Google, and if you will be asking someone like your mother, sister or anyone about Alexa, there are those people do not know that Alexa is existing, so it will not do any effect on your site PageRank, mind as well focus on increasing PR for Google.