Is there a way to append feature classes using a SQL Insert statement, running directly SQL Server, or is it required to run an append in ArcCatalog, Model Builder, Python ...
Possible, but risky unless you really understand how geodatabases are implemented in DBMSs. I would start with SQL and enterprise geodatabases—Help | ArcGIS Desktop and especially SQL access to enterprise geodatabase data—Help | ArcGIS Desktop
This was useful to me, http://desktop.arcgis.com/en/arcmap/10.3/manage-data/using-sql-with-gdbs/edit-versioned-data-using-sql-sqlserver.htm
Craig Swadner (GIS Coordinator)
City of Cape Coral
1015 Cultural Park Blvd.
Cape Coral, Fl 33990
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