Answer
Yes, ArcPad 10.2.3 is compatible and fully supported with the ArcGIS for Desktop 10.4.x and ArcGIS for Server 10.4.x releases.
Current ArcPad Help online resources do not specifically state that ArcPad 10.2.3 is supported with the ArcGIS for Desktop 10.4 release, as ArcPad 10.2.3 was released in January 2015, whereas ArcGIS for Desktop 10.4 became publicly available in February 2016.
Additionally, in February 2016, Trimble updated their Trimble Positions extensions for ArcPad and the ArcGIS Desktop add-in to be fully compatible with ArcPad 10.2.3 and ArcGIS for Desktop 10.4.x releases. Please see the Esri Support Blog topic and Trimble Resources links below if field workflows require post-processing using Trimble Positions Software applications.
Article ID:000013865
Software:
- ArcGIS Server
- ArcPad 10 2
- ArcMap