You can manually add AdSense in a WordPress post above or below the content without any issue. You can simply place the necessary code above, or below, the the_content(); function call. Now if you want to place it within the content, it is a bit more complex.
Most people would install a plugin that will automatically insert your AdSense code into the content of any post. I have used them in the past, but found that it would break the post readability if the code was inserted into the wrong location. Also, some people wish to reduce the number of plugins that are activated in the blog, so a manual method may be better. Once the code is added manually, you can easily monitor your AdSense coverage.