Is it possible to have received the achievement "A Bad Omen: 2048" (Complete the Bad Omen 2048 puzzle) without receiving the achievement "2048 Master" (Score 2048 in the 2048 puzzle)?

Yes, because the target number for completion was only set for 512, I believe.

is correct. We will likely be able to obtain the 2048 Master achievement whenever they add the game back to the site as a regular thing, but I have no idea when exactly that will happen.