Hello @egleckle ...
Publishing a course only grants or prevents access to the course itself. It should not affect any of the things that you are concerned about. I would recommend that you read through the Guide How do I publish a course? ... in particular the bulleted items in the light blue box at the top of the page, especially the last one that tells you when a course cannot be unpublished any more.
Also, you could certainly do some testing on your own with this to confirm what you are inquiring about. For example, did you know that your school has a "test" environment? You can access your school's Canvas "test" environment by following the information in these Guides:
Just also keep in mind that content in "test" might be slightly different than what is in your normal "production" environment (the environment you are typically used to logging into on a daily basis) per the paragraph in the first link under "What happens to my content in the test environment?".
When I let people know about this environment, I always make sure to let them know that after they are done using the "test" environment to log out.
Then, log back in to your school's "production" environment ... again, the normal environment that you are used to logging into on a daily basis. As the first sentence in the first Guide I linked to suggests, "The Canvas test environment allows admins and instructors to test real data without affecting the production environment, such as adding users, testing course content, and/or troubleshooting issues." This is why, in my experience and opinion, it's important to log out of "test" before returning to "production" ... so that you aren't confusing the two separate Canvas environments.
I hope this will be of help to you. Sing out if you have any other questions about this...thanks!