I had the same demand today and I discovered a functional way to solve this.
Firstly, insert the scanned image into your document. I suggest to put it in header, to stay separated from the content (only for control).
Config the image to stay "under the text" (I don't know the correct name in english), so you can carry it without changing your content formatting.
Now, toggle the marks visibility (the icon with a paragraph symbol). Select the image and you will see the mark for "image anchor" aside of his paragraph (an image is always linked to a paragraph). Knowing the paragraph which your image is linked to, select it (all the paragraph) and go for font config (CTRL+D), and select the last option: HIDDEN.
This way, all the paragraph content will be configured as hidden (included your image). But, if you toggle off the marks visibility, all this paragraph will dissapear. To solve this, go to OPTIONS, VIEW, and check the option "hidden text" under "always show this marks" (again, idk the correct name in english, sorry).
This will make your image be showed in visualization, but never in print.
Best Answer
There is an option to print background colors and images. By default, this option is set to false.
From Word 2007, you can find this settings under "Word options" window, "Display" tab, "Printing options" section and the option is called "Print background colors and images".
Source: Office support article.