I am aware that it will depend on die design. I have a 6 ton arbor press, and I think I would be hesitant to think it would manage a fairly detailed die impression, but I have used it for lots of other things including punching round holes in thin sheet metal. I've also got a 12 ton and a 20 ton shop press. Both are air over hydraulic, and actually quite slow. In the field at the "faire" a drop hammer is used. a relatively crude one.
"...a woman dressed in pirate garb at a renaissance fair (or faire if you prefer) place a blank in a set of dies and drop a heavy weight on it to strike a souvenir coin..."
I think if I follow through with this I'll stick with a drop hammer or a trip hammer until production required a faster process.