Does the Apple Battery Case support fast charging?

I’ve got the 30W USB-C charger and I’ve been using it since my iPhone X. I knew it worked with my X and my XS Max, but I just realized that I’ve taken for granted that it works with the Apple Battery Case. Does anyone know if the case supports fast charging? Also, I just realized that I’m not getting the “double chime”, even when the battery case is off. My phone is currently at 31%, I thought that fast charging kicked in until your iPhone hits 80%.
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