IPFS Files – How Long Does Infura Store a File on IPFS?

Note that putting the blockchain (and state etc) on swarm is already planned and thought out.

Integration with IPFS is also in the plan but may have some difficulties. If and when solved this answers your question.

Purely IPFS solution, full nodes can simply add their chaindata subdirectory to IPFS, while light clients download by hash, see this reddit post.

Both solutions need to find a way to reach consensus on the current canonical head block('s hash) which is not trivial.

Also both solutions benefit from an incentive scheme which ensures long term redundant storage.

EDIT: actually as Christian Lundkvist points out, this may not answer the question since "The question asks if we can encode the blockchain data structure into the IPFS Merkle DAG using IPFS objects, so that it is completely linked by IPFS hashes"

The answer to that is that it is easy with swarm manifest trie and a little unclear to me if it is just as easy in IPFS or not

IPFS doesn't solve the persistence problem for you, the only way currently to ensure that your files will exist is to pin them on an IPFS node, which means you need pin rights on that node. Run your own node, there are a few services out there that you can pay to pin content, find a node that will volunteer to pin your content, or wait for Filecoin which solves the problem by allowing you to pay Filecoin for persistence.