Not when they're new, but gradually (depending on how well I'm shooting) the middle gets shot out and then the odd arrow goes through, but just sticks in the ground behind. Then it's time to look out for new cushions. I only shoot recurves and longbows up to 45# - if I had a compound bow it might be different, but then you can put 2 cushions up.
when I was a kid those wattle cup moths were seasonal and everywhere. Haven't seen one for years. We used to call them Chinese junks, which was quite accurate really. I think that's because there were lots of english immigrants where I grew up; many of them were familiar with Hong Kong, India Africa etc. For example, as a kid if someone got in trouble the kids around you would say "amah". In later years I looked this up, and it was the Indian name for nanny. So, I'm guessing these moths were named by English kids who spent some time in Hong Kong.