Definitely Yes, because blockchain as a technology is going to be the biggest disruption after Internet, I believe. It's not necessary for a blockchain to be associated with a crypt currency or a token. Here is a link from IBM, that discusses about several use cases that can be built by Government.
Niti Aayog ( a think tank of Indian Government ) has hired Oracle Corporation this month to implement a pilot project to put the entire stock of medicines made in India on the blockchain with an aim to fight fake and spurious drugs. The project is likely to start by November.
And this is just a few examples, I think, many more can be built on top of blockchain. Most importantly, blockchain can help maintain transparency and that is going to increase the adoption by public faster.