This annotated whitepaper acknowledges the importance of a thorough review:
Constructing a hash function is difficult; constructing a hash function satisfying these constraints seems to be more difficult. This paper seems to have no explanation of the actual hashing algorithm CryptoNight.
Nic van Saberhagen describes loosely some properties of a proof of ...
The question to ask isn't 'Can this be done?' but rather 'Is this something we can benefit from?'.
Since you did ask explicitly if it was possible, I'll address that first:
Yes, it's absolutely possible for Monero to adopt this proposed PoW algorithm. The PoW algorithm is orthogonal to the issue of privacy, as long as the PoW algorithm chosen isn't one ...
Monero uses keccak-256, where 256 refers to the bit length of the hash produced.
Note that SHA-3-256 is slightly different, and so will not produce the same result as keccak-256.
This library will produce the correct hash: https://www.npmjs.com/package/keccak
From my understanding, daughter chains are not as secure. They do not have the same mining strength that the normal blockchain has with its PoW system.
Daughter chains can be helpful for rapid/instant transactions, where I have good faith the network will not be hacked for someone to steal my $2.