Is there an iTunes Visualizer that displays the full song's waveform? Is it possible for iTunes Visualizers to access the entirety of song data in order to display a full, un-animated waveform of the currently playing song? Perhaps the extent of the visualization would be a progress bar that sweeps over the song as it plays.

Assuming this is even possible, does something like this already exist?
I don't think it exists, since Quartz provides limited input for the iTunes track, and mostly real-time.
Quartz is the graphic layer of Mac OS X. Quartz Composer is a tool used to easily create animations, transitions, filters, visualizers, etc that work with this technology. As far as I know it is the only way of making an iTunes visualizer.
When you attempt to create a new visualizer in the latest version, you get a pretty straight-forward of the input you'll get from iTunes:

Here´s a closer look:

There is no file input of any kind. Not even the filename/path, and even if there were Quartz are graphic libraries, thus it's ability for processing data, including sound waveforms is limited. All this input is received in real time, sent by iTunes: Quartz can only receive the numbers/text it is being given in real time, but not actually call any read operations on the sound file, and decode it to a sound wave.
I'll have to say, at least with Quartz Composer, no, it is not quite achievable. I don't think you can create iTunes visualizers in any other way, and I haven't seen a visualizer with such functionality.
Hope it helps!
Kevin