Unfortunately image type will not work. Somethings (like input field height, padding, text line height etc) are calculating dynamically based on icon size, button height and font size. So image would not work here.
That is a shame that it will not work, as I really liked the slide out feature of the search form. The image I wanted to use was quite small, so it wouldn’t have added much depth to the field height.
The screen grab in the link is how I have it set up at the moment and is really close to what I require, I just need to be able to replace the icon with an image the same size as the my account and basket images.