No, it doesn't. It is designed as lightweight format for data storage and exchange. Usually it is used in the context of other GIS applications like QGIS. However, you can also use SpatiaLite to apply spatial functions to GeoPackage files.
But GeoPackage, which the question referred to, does not support spatial functions in and of itself. But I also wrote that you can use e.g. SpatiaLite to apply spatial functions to geometries stored in GeoPackage. But then this is not really different from using any other application like QGIS or gdal.