The answer to your query about whether Fetch as Google will help to increase visibility of your blog is a resounding "Yes!" That is exactly what the Fetch as Google tool does - it gets the attention of search engines. In fact, it is the best way to land your posts onto a reputed search engine results page (SERP) and must definitely be used by a webmaster/blog owner.
Simply waiting for your blog to appear on Google search results may take weeks, months....maybe never! On the other hand, the Fetch as Google tool may take less than 10 minutes, maybe even fewer, to get your blog post's URL crawled.
Note that you are likely to see the message that the URL will be crawled within a day, but you may see quicker results too.