Can users record and interact with their own audio in Articulate Storyline 360?

Take a look at @Nedim's entry in this post:

Storyline 360 Microphone Input | Articulate - Community

He provides an online example that demonstrates how he accesses the microphone and records some audio with a MediaRecorder object, creating an audio blob. This blob can be internally assigned to a URL and then referenced into an audio element that can be added to your SL slide. You could then play this audio element via JavaScript, like any other. 

Quick reference on converting an audio blob into audio element:

https://stackoverflow.com/questions/63521599/setting-audio-element-source-from-blob

To see the details, open Nedim's example, then right click in the white box around the microphone button and select View Frame Source (or This Frame > View Frame Source).

Since he did not share the project directly, I would suggest using the code for guidance and inspiration rather than just copying his code.