He almost certainly wasn't in the smoking room when the ship sank. The witness who saw claimed to have seen him there left the ship in a lifeboat around 1:30 am, so even if the account is true, that was a long time before she sank. And there are other witnesses who saw Andrews helping with the loading of the boats during that time.

The last eye witness account from a survivor stated that Andrews was with Captain Smith on the starboard bridge wing as the boat deck began to go under, and that they both climbed over the forward gun whale and jumped into the water together. I haven't seen any evidence that would outright contradict this being possible, so I think it's the best account we have of how both men met their fates.