How much can the AUC improve comparing the raw dataset and the feature engineered dataset?
Yes, the performance can vary a lot using feature engineering.

Example: suppose a dataset where the response variable $y$  is true if $x$ is odd.

x    y

346  F
13   T
178  F
64   F
987  T
...


Most learning models will fail to identify the pattern and will perform poorly, usually falling back to always predicting the majority class. However simply adding a feature $x \% 2$ to the data will allow any model to perform perfectly.

Of course this a toy example, but the point is that a single well chosen feature can drastically change the performance. Naturally the increase in performance totally depends on the data and the nature of the features added.