How would it improve skills?

Does driving a car improve your running speed?

I have to stretch your analogy in weird ways to make it function within this discussion:

Imagine two people who have only sat in a chair their whole lives. Then, you have one of them learn how to drive a car, whereas the other one never leaves the chair.

The one who learned how to drive a car would then find it easier to learn how to run, compared to the person who had to continue sitting in the chair the whole time.

I've found AI handy as a sort of tutor sometimes, like "I want to do X in Y programming language, what are some tools / libraries I could use for that?" And it will give multiple suggestions, often along with examples, that are pretty close to what I need.

No, but it does improve your ability to get to classes after work