If the organisation you are working with has committed spend with Azure, the future Neo4j Azure marketplace integration would report usage to the Azure portal and burn down the commitment using the organisation's payment method linked with Azure.
Right now, we have the ability for users to sign-up directly on the Aura portal and create an instance which is hosted in an Azure region (which would allow organisations to take advantage of latency and potential ingress/egress savings) - however, this is not tied to the user's account in Azure. More detail on this will be released in the next few weeks - it's a new launch.