I worked with Microsoft Windows Technical Support for a little over 4 yrs. I was also part of the launch of Windows 8, 8.1 and 10. What Reverend Jim mentioned is correct, Windows 10, especially those who upgraded from a lower version of windows, are automatically registered using a Hash of your hardware IDs (don't ask how it is computed, I don't know too). When you reinstall using a downloaded ISO burned on a DVD or from a bootable USB, it should automatically register it as a genuine copy.
So the short answer to your question is YES.