I am also a fan of the Fujitsu ScanSnap product.

The Fujitsu bundled OCR software (ABBYY FineReader) does what you require, retaining the original scanned image with the OCR'ed text hidden 'behind' the image. If I mouse select a word or paragraph the highlighting of the OCR text appears right on/under the original image 'text'. Sometimes the alignment of the image text and the OCR text is not perfect but overall it is usually quite good.

There is a specific setting in my Fujitsu FineReader software to make the OCR engine retain the scanned bitmap as the default is to prioritize small output file size and discard all regions that the OCR engine was able to process.

I did find that scanning at a level above 300DPI did seem to improve OCR accuracy but of course the resulting final file size was also larger since I wanted the original scan images included. I typically use 400DPI unless there are graphics or imagery that I really want to have in high quality.