No, DHT is just a way of determining paths and priority of value lookup by key in the network, so that the load were distributed predictably, while allowing you to find, well, what you are looking for. BTW, while everybody uses Kademlia with modifications, I'd argue that Chord is better for anything related to security and anonymity.

Storage and serving of anything big is another thing. I take it you mean that I2P nodes cache messages relayed via them when the target node is unavailable. That doesn't have anything to do with DHT.