Linking arcgis and postgresql without and enterprise license
Yes. That is possible. You can create a spatial database using PostGIS, and then connect to the PostgreSQL database from ArcCatalog (Add Database Connection). Connect to PostgreSQL from ArcGIS—Help | ArcGIS for Desktop
But can you edit? From what I've read and tried, the answer is no.
Hmmm... I think you got that right.
You can get Read-Only access to the PostGIS data using Query Layers.
For editing, you will need to enable Enterprise Geodatabase, for which ArcGIS Enterprise (Server) License is required.
Retrieving data ...