It should be possible, after all proof-of-work is basically just about spam-protection so in principle any kind of captcha could do. Implementation is not easy though :) Some problems:

1. Block generation rate should be pretty constant and it would be hard to come up with human mining system that has adjustable difficulty. You would also need need to have miners available 24/7 to be able to use the system.

2. System should be decentralized: only shared state should be in the blockchain. How would one generate puzzles/captchas without central server?

Because of these problems I doubt you can have purely human mineable coin that is still useful as a coin. Hybrid coin with block generation done by POW/POS and human miners just generating extra coins could work (I think Huntercoin is pretty close to this). Pretty much only difference to faucets that give out premined coins (or Gridcoin, I guess) would be that the system would be decentralized.