Hi Jerry,
> I have an ArcGIS Server installation. I want to host the 'generate' service with my ArcGIS Server instance so I am not relying on ArcGIS Online. Can I do this?
Since the 10.3 release, Portal for ArcGIS is included with ArcGIS for Server Standard and Advanced. So you would need to deploy Portal for ArcGIS for a hosting server configuration, with the ArcGIS Data Store,
Configure a hosting server—Portal for ArcGIS (10.5) | ArcGIS Enterprise
> If I cannot do this, are there any problems with continuing to use this service for free?
I am not clear on what exactly your workflow is with this statement, can you please elaborate?
Hope this helps,