Yes, it should be able to if someone wanted to.
At present, the best Linux OS support for iPaq PDA is OpenIpaq or familiar if you prefer. It will buid with Open Embedded perhaps in a few weeks or a few months (if the Familiar maintainer finally wake up from his one year sleep).
GPE Opie or Qtopia are the three proposed free Linux desktop for iPaq and SL-5000/5500/5600. Their applications are designed to fit in their small 320*240 screens.
pdaXrom use matchbox desktop, the same desktop as GPE so pdaXrom desktop could run on iPaq. pdaXromuses different applets and better suited windows manager for bigger screen. Only issue so far: pdaXrom applications expect at least 640*480 screens and pdaXrom binary are at present optimised for Intel PXA processors and would just need to be recompiled. Most iPaq running Linux at present use the older Intel StrongARM processor and their screen is only 320*240, so if you were running pdaXrom on them, you would still need to use all tiny GPE applications.
New 640 * 480 iPaq with very fast PXA processors have hit the market but as you should guess none of them have Linux support. Linux porting on those PDA is done by enthousiastic people but all of them only have old iPaq device. I still have an iPaq 3870 but didn't want to buy anything new from HP/Compaq because their new device don't support Linux.
