I don't think there would be a difference in speed.
One advantage a CMS could offer you is caching - "saving" page HTML for a few minutes, hours, or days so users who aren't logged in get these saved pages, instead of pages that execute all the database queries every time a page is loaded. In addition to page caching, there are also other mechanisms available for caching parts of pages.
500ms is a very long time for a pageload. I would suggest you find professional help, since it sounds like you are using a lot of different technologies and are in a rather complicated situation.