I'm not sure if NI will encourage this or not (as it's messing with application resources), but the icon files are stored in a location where they can be overwritten:
C:\Program Files\National Instruments\DIAdem 2014\Resource\BarSource\
The "ResourceDrv" built-in DIAdem variable gets you most of the way there (if you're scripting).
I was able to overwrite NAVDataFinder1.ico with my own .ico file and have the icon come up in DIAdem.
Note that for some reason the icon preview in Windows didn't change, but if you actually open the ICO (or look at the datafinders in DIAdem), the replaced icon was used.