You can unlock Mystery Gift, however, for me it always says, "No gifts were found" from the WiFi option. Anyways, here's how to unlock it:
1.) Go to the Jubilife TV station
2.) Go to the 3rd floor
3.) Talk to the man in the lower room standing next to the woman
4.) When he asks you for the first phrase, type in "everyone happy"
5.) For the second phrase, type: "Wi-Fi Connection"
After that, the Mystery Gift option will be unlocked on the menu screen, with three options: Friend, Wireless, WiFi. I've only ever tried WiFi, and it says that no gifts were to be found, as I mentioned above, so I'm still unsure how it works exactly (if Nintendo even set it up in the US yet).
Oh, and you need to access Nintendo WiFi before the words "Wi-Fi" and "Connection" become available in your vocabulary.