It shouldn’t. If you feel more comfortable, you can wait and re-publish later tonight.
Once that’s done, you’ll just need to add redirect commands to htaccess, so that anyone who goes to http:// gets redirected to https:// @teefers as posted a lot of useful information on redirecting to SSL. Here’s one of his posts with code that should work for you. You’ll need to past that code into an .htaccess file. This can be done in your hosting control panel or through RW. I always use my host’s control panel.