Hi Barney,
Welcome to the Q&A Board.
Unfortunately, the S2 does not imprint the datestamp directly on photos. As you mentioned, the date can be printed out when using direct print.
There are programs that batch process images and imprint the date from the exif data within jpeg files. One such program is freeware called Exifer that lets you mark images by using menu Image/Insert watermark:
http://www.friedemann-schmidt.com/software/exifer/ Please note, however, that you will have to batch process by date. According to the site, "when adding watermarks in batch mode for more than one image, the inserted data will always be taken from the first image only."
Hope this helps.