I’m pretty sure my best axe would cut unhardened chain - it shears through embedded steel nails without damaging the edge. But I’d never purposely hit a chain with a good axe.
A crap axe, sure! I spent most of last week hammering one through pine roots with a sledgehammer. 
But the edge of a crap axe would probably fold.
So maybe the question is really “how craptacular can an axe be and still cut mild steel”?
I just use bolt cutters to cut chain, like everybody else.
