Hi Hector,
Yes, it is possible. You will need to deploy a new site in cloud builder and choose "GIS Server". The option to do this is not available when you choose "ArcGIS Enterprise" to setup a base deployment. After adding a GIS Server to your base deployment or as standalone GIS Server, the Geodatabase button will not be greyed out
Took me a while to figure that out... ArcGIS documentation need to be improved here.
So this way you can register a database with your site. You can enable an Azure SQL Database as Enterprise Geodatabase. You can also register an existing SQL Server database in case you have SQL Server running on a virtual machine. When using Azure SQL as Enterprise Geodatabase it is required to use cloud builder to do this in order to have a fully supported environment.
Cheers,
Ernst