According to the documentation, Esri states "Connections from ArcGIS software to databases in the cloud must originate from machines in the same cloud. For best performance, connections should originate from machines in the same cloud region. In the majority of cases, connection and query performance is poor when you connect from ArcGIS clients installed on-premises to databases in the cloud or make connections between clients and databases in different cloud regions, and connections may time out."
I interpret this as, if you're going to have people in your organization connect to data in the enterprise geodatabase from computers on your network, then you should host your geodatabase on-premise and not in the cloud.
Can anyone confirm, or comment, on this interpretation?
That's a good question! It's worth noting that a cloud-hosted GDB that is accessed through a published service does not experience the same hit to performance. You can even bulk-publish your database layers from a registered cloud connection, then manage user permissions in your Portal.
Are you planning to have users connecting directly to the database? If that's the case, then yes, on-premise is really the only way to go, as the performance hit with direct connections to the cloud are substantial.
I'll echo a bit of what @jcarlson said below but expound on it a bit.
The biggest question will depend on how you are using/accessing the data. Major things to consider:
1. Will I have users using ArcGIS Desktop (ArcMap/ArcCatalog) ? As these require a direct SQL driver interface that does bulk-cursor loading a cloud interface would not be recommended.
2. Will my users be primarily using ArcGIS Pro? If yes and you are working with Feature-Services/Hosted-Services then you will be in good shape.
3. Will my users be using Web-Clients (ArcGIS Online/Portal/etc)? If yes, then you will be in a good place as these all use the ESRI Service-Architecture which is much more forgiving versus the legacy/ArcGIS Desktop APIs.
if you intend to use ArcGIS Pro to connect directly to the GDB Enterprise, you may want to consider using the VDI infrastructures in the same region as the GDB Enterprise.
This way you meet Esri's requirements.
Yes, the software that's talking directly to the enterprise geodatabase should be as physically close as possible to eachother.
So if your eGDB is in the cloud, your Pro users that directly connect to the eGDB need a VDI in the same cloud and region.