Hi @Don Collier ,
there are some differences between Azure ADDS and self-managed ADs you should think about:
https://learn.microsoft.com/en-us/azure/active-directory-domain-services/compare-identity-solutions#azure-ad-ds-and-self-managed-ad-ds
If you have deployed the Azure ADDS you are able to join the domain with your on-premises clients.
Just make sure the DNS is working properly and you routing and network connections are working.
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Regards
Andreas Baumgarten