Just did little bit of research. The “Use maximum texture size” option will display the image at a new maximum resolution of up to 4096 x 4096 pixels. - according to @ChrisDizon
Also, I have tried “Edit texture image in external editor” of the image that was larger than 4096px, and it maintained its original size. Therefore it means, if all of the gathered data is true, SketchUp will store original size and resolution of the image assigned, but display down-sampled version of image at 1024px or 4096px depending on your settings.
Well, this means that I have no point in adding an image larger than 4096px if I don’t want really fat file size.
Can anyone confirm this for me? (I have no way of checking display resolution of image in SketchUp)