The Azur is a gorgeous canvas - especially on the Neverfull GM but as a diaper bag I believe it would get dirty as they are typically put under strollers, in the back seats of cars, etc. If you still are looking into a Neverfull GM, I would look at the Damier Ebene or the Monogram. A few things with those bags as I own both.
The Monogram has a slightly thinner canvas than the Ebene making it more "saggy" or "flimsy" (not by much, but enough to make it look differently than the other), and the Monogram has the uncoated vachetta leather which is prone to water spots, uneven patina due to use, etc. This does not change the structural rigidity of the bag over time, it is just cosmetic.
About the Damier Ebene: when it is brand new, the stiff coated leather handles are extremely stiff and may hurt on your shoulder when the bag is loaded up. Over time, this leather will soften and become more useable. The Damier Ebene canvas has seemed to be more durable in my opinion when it comes to scuff marks and other wear and tear. The nicest thing about the Damier Ebene Neverfull is that because the leather is coated, you do not have to worry about an uneven patina or water stains. I've used my DE Neverfull on multiple occasions when it has been raining or snowing - and it still looks the same as the day I bought it.
Hope I could help, and sorry for the essay I just wrote, LOL!