From what I understand, most recent NLE's accelerate the entire interface using the GPU. Yes, the video playback, on the fly rendering, effects and number of tracks do benefit as well.
But I'm talking about the actual interface of the software is accelerated using your GPU's horsepower. The most obvious example is FCP X, where it seems like all the buttons and the way the timeline behaves, stretching, zooming in and out are all rendered on your screen in 3D using your GPU.
As a matter of fact, even Microsoft Office is rendered in 3D and does use your GPU. Everything is animated now, which makes for a smoother user experience.
Check out this article regarding the
benefits of a good GPU on DaVinci Resolve.
FYI, AVID has a free version of their Media Composer, but is a bit limited of course.