Is it important for the quiet zone of a 2D barcode to have a good contrast to the dark modules of the 2D barcode?

1. Yes, black and white contrast for the modules, background and Quiet Zone is always best.
2. To avoid unintended readability, it is safest to keep the Quiet Zone the same colour as the 2D barcode background colour.

Useful reference:

GS1 2D Barcode Colour & Quality Guide

Examples: