No. The ModelBuilder tool execution history is not saved in the project's geoprocessing history. This is a known limitation. In ArcGIS Pro, the ModelBuilder tool execution history is not included in the Geoprocessing History pane because ModelBuilder involves multiple geoprocessing tools in one run.
To verify the history log of a model created with ModelBuilder, use the ModelBuilder Report view. In ArcGIS Pro, after running the ModelBuilder tool, on the ModelBuilder tab, click Report to view the model's history log.
Alternatively, run the geoprocessing tools separately in the Geoprocessing pane. Use the Geoprocessing History pane to view the detailed information of each tool. To use the geoprocessing tools from the Geoprocessing pane in ModelBuilder, refer to ArcGIS Pro: Automate geoprocessing using history for more information.