Commerce Kickstart on secure server
Yes it should be that easy, Drupal doesn't tend to mind what protocol it's served under. I say "should" because who knows what contrib/custom modules you have that might be doing who knows what, but in my experience contrib tends to be pretty good and you can sanity check the custom modules before implementing anyway. 

You'll probably want to un-comment the http -> https redirect in .htaccess (or implement similar in the vhost if you're using something other than Apache), that way any errant insecure requests will be upgraded before they hit Drupal.

A useful check is to crawl a test version of the secure site (e.g. with Integrity on a Mac) and look for requests for insecure resources. If you see any, you can check the referring URLs to find out where the insecure request comes from (link, iframe, script tag, etc), and use that as a jumping point to find out which module/sub-system is responsible.