Yes, if a Submit assignment is recording the screen and microphone, system audio played into the computer speakers will be picked up by the Submit assignment.
For example, here's a quick clip of audio coming from my speakers for this Submit assignment: https://drive.google.com/file/d/1b4FpXXKv79LU4TgBP2zHygz5hNRTk-WB/view?usp=sharing