You can actually load the data without an enterprise geodatabase license, but the Basic license seat makes the process much more difficult (i.e., generate SQL on the fly to execute in the database through a cursor). However, you cannot use geodatabase relationships in PostgreSQL via ArcGIS without an EGDB.
Note that there are no longer any "SDE databases". The RDBMS has managed the data directly since SDE 3.0, and the SDE API was subsumed into enterprise geodatabase methods in ArcObjects (and ArcPy) long ago (and deprecated at 10.2.2, and removed at 10.3).
- V