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In Bitcoin, one can start mining by just including the header of the previous block into the new block without fully validating it. This is risky, but has speed improvements (being able to start mining sooner).

Is this type of mining possible in Ethereum? What are the requirements? Does the DAG or other hashes involved make this impossible? Or is it equally possible?

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    Interesting question. The DAG, however, is still required. But that could also be generated on a light client based on block height. – Waqar Lim Feb 14 '17 at 9:35
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I would imagine this is impossible because you need the current state in order to produce the correct state root hash for the block you are about to create. More specifically, there is no way to take your coinbase transaction and the previous state root hash (or any other seemingly useful information in the header) and produce a new correct state root hash without having the entire current (as in post-previous block) state. Unless you have another validator instantly send you the current state, it is probably quicker to apply the transactions in the previous block(s) to get the current state.

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