Anomaly Detection System
Yes, your logic and what you are thinking is excellent.

There is only a flaw in your thinking: The variables you run the model with must not necesarily be "correlated" in a linear sense of the word, just don't discard any variable because any of them could explain your binary output, and not have a linear relationship with it.

Is a common solution to binarise an output to detect anomalies, but you will lose the ability to predict "how much" outlier is an outlier, make sure you don't need this information after.