Does Emet-Selch work without the bond with Azem? Yes, he's a fantastic character and ShB is still an enjoyable experience without that context. However, does it add complexity and depth otherwise enhancing not only his character but the interaction with yours? Definitely.

Does Hydaelyn's dialog regarding the Azem crystal make any overall difference? No, not particularly. Does it cause confusion and take you out of the moment because you're asking yourself, "Wait, what? How does that make sense?" Absolutely.

Saying the dialog is the same between languages though is patently false and I'm somewhat amazed at the brazenness given the multiple examples throughout this thread that prove otherwise.