Hi Travis - great question, and an important one too. ArcGIS Server is absolutely set up to use an Enterprise Geodatabase. Your post hits on a few different topics, so I'll try to touch on the different methodologies you can deploy. First and foremost you need to register your enterprise geodatabase with ArcGIS Server. This makes AGS aware of the database and how it should connect. That said, you need to plan on how AGS connects to your database. If using windows authentication, then the account running AGS (in this case ideally a domain account) needs to be given access to the database. If you are using database accounts in your service, then database connections using those accounts (and potentially the version you with to connect to) need to be registered with AGS.
Now you mentioned Portal as well. You can publish to AGS and then register those services with Portal. Alternatively, you can federate AGS with Portal for a more seamless integration. Items published to AGS would automatically publish to Portal as well.
One more note, based on your topic title. Taking this deployment pattern one more step would be using data store as a managed database in AGS. Then in Portal, that AGS instance could be designated as a hosted server. This gives you the ability to have hosted feature services in your Portal instance.
As described above, this is our base deployment of ArcGIS Enterprise (10.5). You'll start seeing more and more of this as the year moves forward.
One word of caution when federating AGS with Portal; Portal will take over the identity management, so named users will be required.
Hope this information helps, and feel free to ask again if this missed your question.
-Adam Z
