What I mean is, is it possible to connect to wifi, go to a dream world, then leave the area with wifi? Once I upload the town is it saved into some sort of temporary memory or will it kick me out once I lose Internet?
I'm fairly certain that you'll need wifi for that. Yes, it is pretty static and nothing is saved but you're still getting the information for the town that you're in. The town's info has to be coming from somewhere, it's not stored on your device. --- Guys... it was announced that there are TADPOLES in AC:NL. This game needs to come out now... if you don't mind, Nintendo of America.
Well, there was one very easy way to test this, and I did so. I headed over to the Dream Mansion, changed into my jammies, got in bed, then headed to a random destination.
I wound up in Ryun's village (hers was the only house there). Snow was on the ground, and she actually had a coffee shop, but no other major improvements. I wasn't even sure that option really existed. I wonder if she hasn't been TTing a bit (for all I know, snow may actually start 12/1, and that's the date in Japan right now), because she had a room with about five winter-themed items, including a "ski resort" wallpaper that I hadn't seen before.
Anyway, we come to the big moment. I located my wifi connection switch on the right side of my 3DS LL and promptly switched it off. Nothing happened. No Resetti error screen, no forced wakeup, no nothing. Just lots of snow in Ryun's village.
I turned the broadcast switch back on, saw it light up yellow, then turned it back off, and made sure the light went off a second time. Nothing happened. With the wifi connection off, I went back to the Anteater, got back in bed and woke up. Everything went normally, and I was back in the village without incident. I turned the broadcast switch back on.
So, now I can officially confirm--once you are already in someone else's Dream World village, you do not need to have a live wifi connection. Thank you.
(P.S. I registered my village on Yumemi's couch, it's 1400-0197-7583, "Wawona". I suspect in the process, I took a snapshot of my village that moment and time which was stored in Nintendo's servers. If you want to visit my Dream World village, all (I think) you need to do is type in this code while getting ready to sleep on Yumemi's bed (code input is the 2nd option). The village snapshot is is obviously so small that it can download in a couple seconds, and hence no ongoing wifi is required.)