This is as I understand it.
When the search engines receive a ping from wordpress about a new post, they hit that post. There is no guarantee that they will look at anything else on the blog. Typically they will glance at the sitemap to see if anything else has been added since they last visited, but there is no guarantee they will look at the other stuff at that time. They might just log it for a future crawl which could be in a few hours, a few days, or a few weeks. It depends on how busy they are.
If you modify a post or a page, the published date does not change so that means the search engines will not be pinged and the sitemap will not reflect that there has been a change to that post or page.
Any sort of dynamic content should always be done in posts, and you should never edit a post to add additional sections to that post. The search engines will likely never find that addtional information until the do a couple dump and reindex of the entire web, which with some search engines happen every three months, but with some it might be six months.
Never change a published date on a page or a post. That will mean that the old URL that the search engines have in their index will return a 404 file not found error, and that irritates search engines to no end.