I love my local setups but FCC reviewers in the current state of the app, might have more trouble reviewing your source code if you develop locally and upload the sites to a static site hosting site like Netlify, Surge or Github Pages.
Now, if you want to be able to do the conversion between local and Codepen, I recommend the following point:
All the CSS files must be copied in order and pasted in the CSS section. If you have any imports put the CSS files in the settings section that allows links to external css files; you can try rawgit for that purpose.
The HTML must be copied to the HTML section but ONLY what's inside the
<body> tag. The head section has its special place in the settings section of your Pen, it even says it in the description: "stuff for
If you have any image tags whose src that point to local files, you must upload those images to an image sharing service and point to them from your HTML/CSS/JS code.