Yes.

Moreover, I don't see why the time spent verifying would be significant. The vast majority of transactions would have been verified by a full node before being included in the block, and then it is just a case of checking the hash, and looking up that the txn was previously mempool verified. The verification time for a block should be insignificant relative to its download time (unless it's a flood attack of new txns by a miner). Or am I missing something?