If you make a plane and move two vertices on opposite corners, you will have a non-planar face. This will be rendered with an "invisible" edge along either of the opposite pair of vertices. Or in other words, the face will be triangulated by picking two opposite vertices.
In 3ds max, there's an option to actually edit this triangulation so that you can decide how it's rendered. This is done without creating any edges, it's just the face's triangulation that's edited. This way you can keep topology in quads while still controlling triangulation:
In blender, I see no other option than to manually add edges, disrupting the topology:
So, is it possible to edit the triangulation in Blender, without modifying topology?