That’s not a problem if you pick up Demon’s Souls on its release date, which is also October 6. However, if you’re lucky enough to procure an early copy you won’t be able Demon’s Souls online until launch day. The single player mode will work fine, aside from a PSN error message when the game loads.
Atlus is shipping a “metric poop-ton” (their words, not ours) of Demon’s Souls in preparation for the October 6 release date. Sounds like there will be plenty of copies of Demon’s Souls then, unlike other Atlus releases.