I have a blog, and I am trying to index the blog posts in a manner quite like SO does. Would this sitemap.xml file act as basically a list and contain all of my blog URLs, or would I have to do something else?
If you're just running a blog, you really only need an RSS feed. You can go ahead and submit that under the sitemaps tab in Search Console.
You don't need a sitemap unless you've got like 10s of thousands of pages and/or you're an e-commerce site. Most WordPress SEO plugins gen them automatically, so it's not much to provide it just in case.