Couldn't you do that manually with a simple downscaling filter? I'd be very shocked if fragment shaders did not have a min or max function.

Repeatedly shrinking by a factor of two means log2(max(width, height)) passes, each pass is a quarter of the pixels of the previous pass so that's a total of 4/3 times the pixels of the original image. Should be low enough overhead, right?

Sure, that will work, but it's log2 passes + temp framebuffers. As for overhead, I'm afraid it will eat a couple fps if you run it on every frame. In practice, though, I'm not sure that finding the exact maximum is that valuable for rendering: a good guess based on the dataset type will do. For example, if you need to render N points that tend to congregate in the center, using sqrt(N) as the heuristic for the maximum works very well.