It will help as the kit is essentially some sand paper, polish, and depending on the kit, some clear coat. As you would know, with sand paper, you will be taking off as much as you want (time + effort). Just keep sanding until it is smooth to touch then start polishing. While you're at it, consider sanding off the markings as it will give you a much cleaner look (though leaving the circle towards the middle isn't a bad idea as if you get the professionally leveled, they will use it as the 'focus' point. Not necessary though).

I recommend getting a kit that includes the clear coat (often called the 'protection coat' - Same crap) as this will prevent you having to do it every few months. You can make your own kit to save money by buying some 400 grit, 800 grit, 1200 grit and 2000 grit (feel free to skip some of these steps however I'm a bit OCD. I even start with the 800 grit even though it takes longer I prefer to be safe), and some plastic clear coat. Everything can be found at bunnings.

Good luck and post up your results! Even if you ended up just buying some. Really though, it's honestly not much work at all. Get a mate to hang out with or listen to some music. Will be done before you know it!