yes you need wifi to use club tortimer. club tortimer is essentially the same thing as the regular island, but instead of it being your own private island, it's a public island where you and up to three other randomly selected players can hang out. sometimes you meet really cool people and sometimes you meet bratty kids so it can be a mixed bag.
there are also rare items that can only be found in the club tortimer gift shops, so if you want any of those items badly enough, CT can be worth it (though it's probably easier to just ask in the trading forums if anyone can get you one). I couldn't find a list with pictures, but if you google it, you can get a general idea of what you can find.
Visit my dream towns!
Angie from Maplerow, Ranae from Wayfield and Olive from Yorkwood
This guide has a lot to say about the island, including Club Tortimer. The Item table at the end shows which items are Club Tortimer exclusives, and which items can be found on both your private island and on Club Tortimer. You can find this guide right here on ACC, in between the other AC:NL guides that you can access in the left sidebar under the "Gameplay" section.
Tiptoe through the window, by the window, that is where I'll be
Come tiptoe through the tulips with me
Like others have said, it is a mixed bag. Personally I don't think I'll get it again. I lost my originally town to corrupt data over the summer. And while a small thing, I do not miss having to tell Kapp'n whether I am going to my Island or CT every time I head into the boat.
and soggy steamed vegetables are the universe's way of crying inconsolably.