Yes, but it's a very manual process. You copy/paste your code into the relevant editor area and click the
assets button at the bottom to add images.
If you're using external libraries, you should be able to add them in
Nobody said you're forced to use Codepen. You can actually put your projects anywhere so long as the code can be viewed and the project runs live. You could push your project to Github (for code review) and then use the Github Pages feature to display the running project.
If you aren't doing most of the work in Codepen, save yourself some additional work.