I don't have my Kindle with me at the moment, but I do know that I had to update the time (page 2 or 3 of the settings, when accessed from Home) after we switched to Daylight Savings. I definitely had wifi on, and it did not pick up the time from there.
I can't really address the "have to register first" issue, since I didn't even realize the Kindle had a clock until after I registered.