Many mobile devices require the image to be of limited dimensions (2048x2048 on most, 1024x1024 on older devices), power-of-two in size, and if you use compression, the image must be square for PVRTC. Black means the texture is not usable on the device.
What do you mean by "very large images"? Whatever the size of the texture you imported will be the size of the sprite when added to the atlas. So if the source texture is 2500x2500, that's what you will see in NGUI as well.