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How would multiplying all of the predictions from a given model by 2.0 (for example, if the model predicts 0.4, we multiply by 2.0 to get a prediction of 0.8) change the model's performance as measured by AUC?

No change. AUC only cares about relative prediction scores.

Yes, AUC is based on the relative predictions, so any transformation of the predictions that preserves the relative ranking has no effect on AUC. This is clearly not the case for other metrics such as squared error, log loss, or prediction bias (discussed later).

It would make AUC terrible, since the prediction values are now way off.

Interestingly enough, even though the prediction values are different (and likely farther from the truth), multiplying them all by 2.0 would keep the relative ordering of prediction values the same. Since AUC only cares about relative rankings, it is not impacted by any simple scaling of the predictions.

It would make AUC better, because the prediction values are all farther apart.

The amount of spread between predictions does not actually impact AUC. Even a prediction score for a randomly drawn true positive is only a tiny epsilon greater than a randomly drawn negative, that will count that as a success contributing to the overall AUC score.