Of course they could. What would be stopping them? It wouldn't be the same though as the currency would be centralized and that's not what we want. I'm sure cryptos will influence the future of money in some way though.
The hypothetical cryptocurrency mentioned in the article posted by OP has a mix of centralized and decentralized characteristics. The Fed won't have special powers and it won't have the ability to remove or add entries in the blockchain. However, the currency would be 100% premined and distributed and redeemed via centralized channels rather than distributed in a decentralized manner as in the case of Bitcoin.
They probably wouldn't create a cryptocurrency, but they instill a sense of transaction verification (i.e., blockchain) technology to decrease the ability to counterfeit the dollar. I don't see them replacing the dollar and what would a second currency, a crypto currency, do for them or the US?
No, it can't. No way.
It would be totally illegal.
The Federal Reserve, nor any central bank, doesn't have the power to create a new currency. It's duty is to protect, or control, or develop (depending on circumstances) the currency which is legal tender in the country. It cannot create a new currency, and it cannot change the currency it's working with.
It's not really a replacement for the dollar or even a new currency but rather a digital representation of the dollar that is able to leverage the power of the blockchain to allow or trustless, near-instant, and low-cost transactions. The Fed will keep the coin's value stable by readily accepting USD for fedcoins and vice versa.