Your question is pretty much semantics. "Pushing" ISO 100 film to ISO 400 means you underexpose by two stops when shooting the film and then "push" the development to compensate. Although not many people actually refer to it as such, when you "push" film in development it is because you "pulled" the exposure when shooting the film. Most people just say they "pushed" the film.

In the case of your example, this would usually mean you put ISO 100 film in your camera, set your meter for ISO 400, and then use the recommended values of the meter set at ISO 400. This would result in the ISO 100 film being underexposed by two stops.

But if, as stated in your question, you increase the recommended exposure of the meter set at ISO 400 by two stops you are then exposing exactly the same as if the meter were set to ISO 100 to begin with! So you haven't really pushed anything when exposing the film. You've shot your film at proper exposure for ISO 100.

The thing one must understand is that changing the ISO setting on a film camera does nothing to affect the sensitivity of the actual film, it only affects the calibration of the camera's light meter to account for what you are telling it is more sensitive or less sensitive film.