As of the time of posting there is no direct use of the NavCards. The NavCard from Transit can be accepted into the build table in Die Rise. There is no NavCard table in Mob of the Dead. When you use the Tranzit NavCard in the Tranzit NavCard Reader you get the message
"That is the incorrect navcard!"
However when you use the Tranzit NavCard in Die Rises' Reader you get the message
With absolutely no visible affect to anything within the game. As of now, this is all we know about NavCards, the rest of this answer is speculation based upon comments the developers of BOII Zombies have made.
! The developers have confirmed that there will be an 'end game' to BOII zombies. There is a way that the 4 main characters will be able to escape the zombie apocalypse. Further speculation leads to this happening after they have released all map packs and you have linked each map together using the Navcards. The reason that no Navcard works in the Reader in Tranzit is because after the release of the final map, the Navcard from that map will work in Tranzit's reader to enable the 'end game' content.
! The reason that there was no Navcard table in Mob of the Dead was because it did not involve the greater storyline with the 4 main characters. Similar to Call of the Dead in Black Ops I.