I don't quite understand how you can expect the screen to keep displaying a calendar when the calendar program has closed. I cannot think that is posible, unless it is saved to the wallpaper's picture file itself.
yes it is possible..that's also what i meant by 'print'.

check
BGInfo by sysinternals. It let you display your system info on desktop wallpaper. first it grabs your current wallpaper picture and print/paints important info about your system on the pic then re apply it as your desktop wallpaper.
http://img.microsoft.com/library/media/1033/technet/images/sysinternals/images/screenshots/BgInfo.jpg
by the way, i found an online tool
here that can paint calender on images you upload. it can also accept image on flickr, photobucket or other online sources.

http://bighugelabs.com/flickr/output/wallpaper7922329.jpg
not so bad i guess..but if there's offline tool to do exactly like this, that would be much better
