From what I have gathered with the Buzztouch site, it seems to create basically a web app. Will apps created with this still work if they are not connected to data (i.e. an iPod Touch not on WiFi)? Obviously some features would not work if not connected to data, but would the bulk of the app data stay on the device?

The answer to your question in a single word is YES. Well most of the apps created with the bt are online apps but if the developer wants to create an offline app then its possible too. All you have to do is store all the files in local storage instead of storing it on server or dropbox.

Thanks! I'm sure I haven't gotten to that lesson yet in the U since I'm just getting started, but is that a setting and/or will I need to self host my apps to do that?

To make an app with local contents does not need to get self hosted. But thats entirely your decision. What you have to do while creating your app is that put all the necessary files (image files, docs, pdf files, html files, video files, etc.) in respective folders. Also in your control panel while creating the screens for those files remember to fill the fields locally rather than filling the fields of url. This approach will make your app heavy in size but that is doable since the users will not again need to connect to the network every now and then once they download your app.

Thanks again! Very helpful.