No, ArcGIS Pro does not require Java data installation on the machines it is installed on. The ArcGIS Pro installation comes with a folder at the C:\Program Files\ArcGIS\Pro\java file path, which contains Java components packaged to run ArcGIS Pro without needing to install Java on the machine. When ArcGIS Pro is downloaded on a machine, it automatically installs or removes Java components as necessary. The items packaged in the C:\Program Files\ArcGIS\Pro\java folder are listed in the Open Source Acknowledgements spreadsheet. For more information, refer to Esri Legal: Open Source Acknowledgements.
Additionally, ArcGIS Desktop add-ins can be created using Java, but ArcGIS Pro add-ins are written in the C# programming language using the .NET framework. Before installing ArcGIS Pro, install Microsoft .NET Desktop Runtime 6.0.5 or a later patch release. For more information, refer to ArcGIS Pro: ArcGIS Pro 3.1 system requirements.