Without HEAD loading first there can be no BODY.
Before your BODY gets rendered, it has has to be loaded first. And if it is loaded, then the HEAD has already been loaded.
You're probably interested in whether a browser can load simultaneously both CSS files and the HTML document itself. It will depend on the browser implementation, but I believe most can download at least two documents simultaneously.
One other important thing is that the more files a document consists of, the more chances the request for one of them gets lost. So by using inline CSS you make sure the CSS never gets lost.
But I must point out that inline CSS is considered a bad style. Once you have a sufficient amount of markup, you will find it increasingly difficult to update your pages all at once. You will inevitably be losing one or the other instance. It is a much better idea to declare all styles in a separate document and reference them from pages. This way, when you need to change some color, you do it in one place and not in 37 places to be found in your pages.