To what extent is my interpretation of computable numbers correct?

Question

Interpretation: Consider the comic strip below, where a person tries to prevent a robot from dismembering them by asking the robot to compute $\pi$ - the robot quickly produces an algorithm to calculate all of the digits of $\pi$ and begins dismembering the person. This is possible because $\pi$ is a computable number.

In contrast, if the person had asked the robot to calculate Chaitin's constant (assuming the robot didn't say something like "which Chaitin's constant?" or "insufficient parameters") or some other non-computable number, would the people have been able to escape the robot's dismembering?

As far as I understand (1)(2), the robot could make an algorithm to calculate the first $n$ digits for any $n$, but to attempt to compute "all" of Chaitin's constant would take an infinite amount of time, because each new digit would require a new program, or something like this.

Question: Is this interpretation at all correct or am I completely off the mark here? To what extent could one describe computable numbers as numbers which "prevent a robot in this specific situation from dismembering people"?

I.e., do all non-computable numbers have algorithmically random (decimal, binary, etc.) expansions?

Source.