Will activating a different theme preserve custom settings to current theme?

I have theme A currently active, and theme A has custom settings (like header image, custom CSS, etc). I am having issues with theme A, and want to activate theme B while I troubleshoot these issues. If I activate theme B, and go to activate theme A later, will my custom settings be preserved?

Yes, your options should be preserved unless your themes are really bad and doing it wrong.