Yeah, Alex Kidd is a Christmas encoded free gift, but since you can only change the time when not connected to xbox live, you can only use him offline by setting the consoles time till christmas or after.
Cool. If I unlock him offline though, will he stay unlocked upon going back online?
If you went back online, your Xbox 360 restored the time and date, so that made Alex disappeared if you do. So stay off until Christmas is your best bet. --- I used to be hearing person like you, until I took the fever in my ears. ~FredCat