To answer your question, yes. The Ginda region has it's own PC storage system, though it is also the only one NOT connected to the other PC systems. It also has more limited space, but that will almost never get brought up. Basically, if you travel to Ginda, the only Pokemon you have when you arrive are the ones you bring with you. You can't access Bill's PC and pull out another one. Likewise, if you're from Ginda and travel somewhere else, then you can't access the Ginda region PC system, so you have to catch new Pokemon and use their system. All other regions are connected, but Ginda doesn't allow foreigners in very much, and doesn't like it's natives leaving often, since they don't want the Gijinka population to become threatened.
Another note, all the towns in Ginda are to be named after Alice in Wonderland character/places, with the starting town/port city being "Cheshire," and the final town being "Alice."