How different culturally would the Dutch have been from Germany versus other parts of Germany; for example, would the Dutch be distinct in a more signifigant way from say Saxony or Hanover as Allemanic or Austo-Bavarians?
About the same, actually. Though Saxony and Hanover had their ruler classes speaking Hochdeutsch for quite a long time, so it was probably a bit more in practice. Of course, in the Burgundian Netherlands, the official court language was French, but nobody outside of the Walloon provinces (Namur, Artois, Hainaut) was very pleased with that, to put it mildly.
Of course, cultural differences are less important depending on the political reality. Frisia was very different from Holland, and Groningen and Drenthe both differed a lot from say Gelre, but they still banded together due to outside pressure. And on the other side, the area around Cleves was strongly Dutch-speaking (bar a few enclaves) but never ended up in Burgundian possession, and therefore became separated from the Low Countries. And I hope I don't have to tell you people about the various attempts by the Union of Utrecht to seek out French or English protectors.
So, when you're talking about the 16th-century Low Countries and how to stretch it out, you've got to talk politics, not culture. Which rather opens things up a lot, I find.