Provided you create a custom menu and include dynamic categories and tags pages as items in it - yes.
The whole bar is the custom menu. There are multiple items one can include in the custom menu bar. It's critical that you comprehend the differences between Pages and Posts http://en.support.wordpress.com/post-vs-page/ and you are clear on the fact that static Pages are not Categories and are not Tags.
(1) There is only one page we can post to in any blog and
(2) The static pages http://en.support.wordpress.com/pages/ we create do not automatically update.
Only the dynamic pages like Archives, Categories and Tags created by the software when we publish a post will update automatically update with new posts.
By default the front page of the blog is the post that displays all posts in your blog. Though there is only one dynamic page in a blog for posts (not pages) http://en.support.wordpress.com/post-vs-page/ and we cannot post to more than that one page, we can create the appearance that we have posted to more than one page.
We organize posts by assigning categories to them. You can create a custom menu and add the dynamic categories pages into the custom menu.
There are many common errors, misunderstandings and misconceptions when creating custom menus and there are some tweaks you can use to improve your custom menu as well.