I did this. See our pretty new lock up in the address bar? I managed to do everything in the right order, and it took about 15 minutes only because there's a little delay in the certificate hooking up, but other than the site slowing down for a few minutes, I don't think it was even noticeable. I didn't even have to log back in, but some people might. It's technically a different site with the "s" added to the URL.
Some internal links might or might not be broken (like if someone linked to an old post) but I added some code to redirect "http" requests to "https", so it might not be a problem. We'll see.
All done as far as everyone but me is concerned. I have a few administrative things to do but none of them will affect the user experience.
If I knew it would be that easy....
Don't look at me, I just work here.