The answer is no, you can't manually edit navmesh vertices.

As usual, Unity's built-in solutions are very rigid and narrow in their application.

Your best option for this would be to create a physics mesh specifically to be used with the navmesh, put it in it's own layer, then set the navmesh surface to target that layer only (Object collection -> Include layers). There are addons in the asset store that allow you to edit meshes in the editor if you want that functionality.