Seeing as the video editor has become as powerful as it is, it would be great to use it as a stand alone video editor.
Does such a build exist?
In Short, No. You can make blender builds without many features (collada, game-engine, freestyle, smoke etc). But you can't make a video only version of Blender.
I'm almost completely sure there are no builds with just the video editor, but if you wanted to use it primarily as a video editor, you could set the video editor as the default view when blender is loaded up.