I think you are asking if you can have a quad where at least one of the points is in a different plane. The general answer is "no". For many file formats, all quads must be triangulated.
A manifold surface area encloses a volume(where the chosen material solidifies) Since a face/quad/tri has no thickness,No volume ,it is not recognized as an object unless it is part of a manifold surface enclosing a volume. Consider the surface area a bubble, containing the volume where the material is supposed to be