Down rating your film does only one thing: changes exposure (increases it, to be more specific) across the board, meaning in all shots in which the rating is used. The only thing rating a 400 film at 200 does is to apply a built in exposure compensation of plus one stop.
So, in short, the answer to your question is YES. When you increase exposure to change the density of certain areas of the film, every other area increases along with it. Since the whole frame is exposed all at once in the same exposure, this is how it must be.
Changing development simply changes contrast. This is true within a certain exposure range, in any case. In an instance of the contrary, an extremely unexposed - i.e. mostly blank - negative won't really have it's contrast changed in a significant way even if you develop it forever. However, as long as there is above a certain threshold of "meat" on the negative ("meat" meaning exposed silver halides), the general statement I made holds true.
In short, the light in a scene and the exposure setting used to control your film's exposure to that light determine how intensely the silver halides are exposed. Development controls the densities at which metallic silver is formed from areas of silver halide that have received a certain amount of exposure. The more exposure to light a silver halide has experienced, the faster it will convert to metallic silver upon development. This means that the amount of exposure you give to certain areas not only affects their final density, but effects how quickly the developer will act on certain areas of the film.
To say it again another way, more exposure to light makes a silver halide more sensitive to developer. Since any pictorial negative has areas that have received more exposure than others, and other areas that have received less exposure than others, there will always be areas of the negative that are more sensitive to development than others. Thus, variations in development time on any negative containing more than one tone must vary contrast. You see that exposure and development are a "team" that work together to determine what you get on your negative.
In general, I think it makes much more sense to simply use box speed, learn the contrast you get on your film with different developing times, and to simply manually overexpose your film only in shots in which overexposure would be beneficial, not to automatically over expose every shot by downrating the film. Overexposure does not benefit every shot, though this seems to be a prevailing belief among photographers shooting negative film. Overexposure can be more easily adjusted for in printing than underexposure, so it is generally better to be over than to be under. However, this is not the same thing as saying that overexposure is good for every picture. It is not even close to the same!
The thing that rarely seems to be driven home in all this re rating stuff that flies around among photographers is that you must develop an eye for luminance range in your compositions, and/or use a meter to measure it, and that you must also learn what luminance range a film can capture when exposed and developed in various ways. There is no magic bullet film rating and development that will work across the board in every picture you take. You need to know your light, know your film, know your process, and learn how they all come together so that you can manipulate these three things to get what you want when printing.