The Mechanical application will publish geometry parameters as well, but it only if the geometry source is a CAD system and not from the DesignModeler application.
From DesignModeler: The Mechanical application will neither publish parameters from the DesignModeler application nor display them in its Details View. Publishing of the DesignModeler application parameters is handled solely by the DesignModeler application.
From CAD: The Mechanical application will list the parameters in its Details View, where you can manually choose to publish them to Workbench. The CAD parameter values will be read-only in the Mechanical application. To change them, you must promote the values to Workbench.
  |
| Ansys Workbench |
 |
| Mechanical |