Does Voice Dictation on the New iPad require a network connection? Does the the new iPad's voice dictation require a network connection? I ask because Siri does require an active network connection and I am wondering if voice dictation works in a similar manner.
Yes.

With many methods of voice dictation, what happens is that your voice is recorded and digitized, and your speech is broken up into phrases which are uploaded over the Internet to a powerful computer server which translates your speech into text and then transmits the text back to your device.

However, there is a long history of programs for Mac and PC which perform voice dictation and transcription entirely on your Mac or PC without using an Internet connection.

I don't know of any apps for iOS that perform voice transcription entirely on the device without using a connection to a server on the Internet.