Hello @dtpeter2901,
I am sorry my initial response did not answer the question about "Has Autodesk produced any documentation on how to use the desktop connector to sync files to BIM 360 docs?"
The Desktop Connector is not used as a syncing application. From the Desktop Connector help documentation, in the "What Is Desktop Connector?" section it provides the following description:
"Desktop Connector is a desktop service that integrates an Autodesk data management source (or data source) with your desktop folder and file structure for easy file management.
The files in the data source are replicated in a connected drive. You can manage files in the data source through the connected drive, just as you would any other folder on your machine. Changes made in the connected drive are automatically uploaded to the data source."
That said, there is no feature parity (from a synchronization perspective) between Buzzsaw Sync and the Desktop Connector. The functionality you seek has been requested and posted to the BIM 360 Ideas page as feature enhancement request. I recommend you "Vote" for each of the ideas linked below. There more votes the ideas receive, the chances of this functionality being added to the product increase. have gone ahead and voted on both while drafting this response.
With regards to a useful page or resource to use the Desktop Connector, the in-product help is a great source of information on how to use the tool. It even includes the User's Guide for Desktop Connector as shown in the screenshot below.

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Regards,
mespaillat
Autodesk Support Team