@Josh Lynch , Thanks for posting in Q&A.
From your description, it seems you want to disjoin the device from Azure AD and then register to Azure AD. If so, I think the device needs to unenroll from Intune. Then enroll again. When we do this, the device ID will be changed. So the device will be different.
In fact, when profile is removed from the device, some CSPs remove the setting and some CSPs keep the setting, also called tattooing. Based as I know, BtLocker setting will not remove from the device. Here are some articles for the reference.
https://learn.microsoft.com/en-us/mem/intune/configuration/device-profile-troubleshoot#what-happens-when-a-profile-is-deleted-or-no-longer-applicable
https://www.anoopcnair.com/intune-policy-tattooed-not-tattooed-windows-csp/
Note: non-Microsoft link, just for the reference.
Meanwhile, for Azure AD registered device, based on my research and test, you will use local account to login. Only Azure AD joined device can use Azure AD account to login. For Hybrid Azure AD join device, we will use domain account to login. You can see more details in the following link:
Azure AD registered devices
https://learn.microsoft.com/en-us/azure/active-directory/devices/concept-azure-ad-register
Azure AD joined devices
https://learn.microsoft.com/en-us/azure/active-directory/devices/concept-azure-ad-join
Hybrid Azure AD joined devices
https://learn.microsoft.com/en-us/azure/active-directory/devices/concept-azure-ad-join-hybrid
For the AD account login, I think this depends on if the device is still domain joined. If yes, I think the previous domain user profile is still there. And the device can be login using AD domain account. I think "azure-ad-hybrid-identity" support or ADFS support may give more help on this question.
Hope the above information can help.
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