Sounds like you want to solve persistence and connection issues by using peers to store a distributed global server/client state.
I can certainly see upsides to an MMO that didn't need any server infrastructure at all and a blockchain or similar solution could probably be made to work, but it wouldn't be simple to convert the game to use it, and the client storage requirements would quickly become significant.
Intriguing premise though.
If I getting you right you want to do something on the cryptocurrency type world and want to trade currency to other players. That I have to say no. Because it promotes Bots and such.
Cryptocurrencies usually use blockchain ledgers, but blockchain in no way implies cryptocurrency.
What a blockchain could do for a peer-to-peer game is allow the peers to also be the core authentication/transaction/chat/mission/update/whatever servers, while maintaining or improving upon security/resistance to tampering. You could track all instance states and validate them against other peers. Loads could be balanced better, peers obfuscated better, and anomalies would be rejected by the network. It could make the game much more resistant to downtime, enable persistence we cannot practically have in the current system, and prevent cheating much more easily. You could probably get all of the benefits of having dedicated servers, while making the game even more distributed decentralized.
Downside would be each client having to act as a node which could require significant local storage if the entire blockchain were kept. There would also need to be Frontier superpeers to push through changes (patches) against network consensus.