Quite possibly, due to the size of a shotgun firing pin and the small hole for the percussion cap, there would be very little, if any gas escape.
Excellent idea and not difficult for someone with a lathe to make up these cases for normal primers.

Turning a case with the central pin for firing a percussion cap would be much more difficult.

I read an article years ago, might have been Gun Digest, or Guns and Ammo Annual, wherein a fellow was turning cases for his .577/450 out of brass and having a narrow, .45/70 sized internal powder chamber, so he used standard .45/70 data. No sizing and ever-lasting cases.