Is it accurate to say that SHA-3 (keccak) is based on Merkle-Damgård? I know that sponge functions are different in many ways. Yet I'd like to know if SHA-3 can nonetheless be said to be "based", if not simply "inspired", by the Merkle-Damgård construction. To be more precise it seems to be a wide-pipe construction followed by an entropy collection procedure.

Is it accurate to say that SHA-3 (keccak) is based on Merkle-Damgard?
No. That is about as accurate as saying that airplanes are based on motorcycles, because they both have engines.

In MD, the input to the hash is converted to a key, which is used by a block cipher to encrypt the initial value, then the entire encrypted value is the hash.

In a sponge based hash, the input is XOR'd into the initial value, then the entire value is ran trough a permutation, and finally a small piece of the permuted value is used as the hash