A:Answer laurel,
The metal tip of this adapter extends approx. 6.5 mm (approx. .25 in.) and is designed to fully engage the USB-C socket. I worry that any significant case thickness will prevent proper electrical connection. Sorry I can't be more definitive.
As shown in your photo, there is a plastic shoulder to the adapter tip. If the case opening can accommodate that shoulder or be enlarged to accommodate that shoulder, there is a decent chance that this adapter would work for you.
Bon chance.