The A16 insert has a smaller pressure plate than a 12, but the gearing that determines if you get 12, 16 or 24 exposures is in the back. Your likely result would be 12 or 24 frames with soft corners, depending on whether you load 120 or 220.
I don't have a 220 back, but mechanically, a 16 insert goes into a 12 back fine, so, from what I can tell, the answer to your question is "yes", but it won't get you to where you want to go.
FWIW, I've heard of people successfully using 120 in their 220 back, I think you have to align the start mark differently, plus remember to stop shooting when you get to 12. The spacing is off as well, as I recall.