I asked about this a while ago on a PS2 forum since both PSX and PS2 memory card used the same pinout and PS2 format was different but shouldn't be a problem with the Dex Drive. Sure enough, the Dex Drive can use PS2 memory card with no mod, just a different program to handle PS2 format.
http://moberg-dybdal.dk/psxge/ (this also supports other memory card reader as well)
Worth checking out if you have a Dex Drive gathering dust and you want to make a backup copy of PS2 memory card or are running out of room on the memory card and don't want to delete anything or buy new memory card.