Update! So this is already done (of course). StegMark is the name of a product that will do this and which is e.g. implemented in certain HP Scanners, among a host of other products.
Original post: There are a number of scenarios in which it may be beneficial to have a scanner automatically add a watermark to a scanned image.
Example: A scanner is used at a bank - images should be "stamped" with "Sensitive - do not distribute". Or a date stamp should be applied, etc, etc.