Yes, as with our current version of Insights for ArcGIS version 2.1, which has geodatabase support for Oracle and SQL Server, we plan to implement the same for PostgreSQL.
We still definitely plan to support Postgresql (PostGIS and ST). This slipped from our original target data mentioned above. I estimate our release in Q1 2019 will have this feature.
Do you have any launch date ready for this support? Just to confirm, we will need the PostgreSQL built as an Enterprise Geodatabase to fully support this?
Our Insights 3.2 and 3.2.1 release will be available within about a month. It will require ArcGIS Enterprise 10.7 (Insights 3.2.1) or ArcGIS Enterprsie 10.6.1 (Insights 3.2). Both of these will be released at the same time, in a few weeks. They will support connecting to native PostgreSQL using their native spatial type, or the esri spatial type. It can be a geodatabase, but it doesn't have to. So no, it does not need to be an Enterprise geodatabase. Does that answer?