Activity: Learners have to click at a specific time during an audio clip

Without looking at the specifics of your activity, it certainly sounds entirely possible.

My initial reaction is that I would have the audio running on the base layer.

I would then start a layer (Layer 1) with my 'Stop' button (Button 1) on it as I start playing the audio:

i.e Show Layer 1 when the timeline reaches 5s

At the 'correct' time they should press the button I would display a second layer (Layer 2) with an identical button  (Button 2) in the same position. By setting this layer to "Hide other layers' it will automatically hide the first layer when displayed.

So I set a trigger that says Show Layer 2 when the timeline reaches 20s...

Let's assume they have just 4 seconds to press the button. After 4 seconds I hide Layer 2 and display Layer 1 - e.g. a trigger on Layer 2 that says:

Show Layer 1 when the timeline (on this layer) reaches 4s

I would need to make sure Layer1 also had 'Hide other layers' set so it automatically hides Layer 2

If the learner presses the button between 20s and 24s they would be pressing Button2 and you could pause the audio at that point and give whatever feedback you need to

If they press the button outside that time range they would be pressing Button 1 and you could take the necessary action triggered by that button.

I'm positive someone else will come up with a brilliantly simple  and way more elegant method of doing this, but, in answer to your question, I would say yes! Storyline could do this...