@AdamChristman-3441, Thanks for posting in Q&A. For your question, I would like to say yes, the owner of the computer will need to be changed to the user of the computer which has both Microsoft Intune and Microsoft Entra Premier license assigned.
Also, automatic enrollment is needed to configured for these users. We can set MDM user scope as All or some which include all these users.
After that, we can use the script mentioned in the following link to trigger the enrollment. As a note, this needs admin permission and the script needs to be run under system context.
https://call4cloud.nl/enroll-existing-entra-azure-intune/
Note: none-Microsoft link, just for the reference.
For new devices, you can consider Autopilot enrollment. Or if these existing device accept to reset, they can also use Autopilot as a good option to enroll into Intune.
https://learn.microsoft.com/en-us/autopilot/tutorial/user-driven/azure-ad-join-workflow
Hope the above information can help.
If the answer is helpful, please click "Accept Answer" and kindly upvote it. If you have extra questions about this answer, please click "Comment".
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.