No, the version of Python that comes installed with various ArcGIS products cannot be upgraded. To upgrade the installation of Python, the version of the product must be upgraded.
This includes but is not limited to the ArcGIS Python API, ArcGIS Pro, ArcGIS Desktop, and ArcGIS Enterprise.
It is not supported, under any circumstances, to manually upgrade internal components of any part of the ArcGIS Enterprise software stack. Esri issues new releases and security patches for existing releases on a regular basis to address vulnerabilities that are found in the software.