It will make no difference what so ever.

As long as you structure your site sing optimised headings and fill your content with keyword variations you should be good.

Adding a category to the side bar is no more effective than adding your keywords in your main text.

No categories are not needed if you are making a minisite with WP. I do it all the time. In fact this is the method I use all the time now because it does wonders in the search results.
I typically create my main page as a static page and all other pages as post pages.
There is only one problem when you use your post menu I think you are limited to 15. If you need more than that you will need to do a little php editing which is real easy and you can up this to whatever number you need. Most of my sites are bellow 15 but I have a few that are over 20. Then you can turn off the categories widget and click the box that says no comments and basically have a website that looks like a regular website.
The nice thing about using post pages instead of static is when you submit your RSS feed to RSS directories gives your site a good boost. I also highly suggest using google analytics and any new search terms that show up there that are more than just an accasional search use it to update you meta keyword tags. If you want to do even better check out "all in one SEO" plugin it is free.

So based on my testing and the above technique not using categories for SEO makes no difference. In fact in the last year I have quit using HTML editors and other CMS and all my sites are not based on this technique. My main interest was having an RSS feed available and a technique where I could build a mini site built and submitted to RSS aggregaters in under 2 hours once I have my content and templates.