Yes. That would be a feature request. Shotcut can do it, but not automatically.
The steps to do it in Shotcut would be:
- Open the file in Shotcut
- Extract the subtitles
- Add the clip to the timeline
- Import the subtitles in the Subtitles Panel
- Add the Subtitle Burn-In Video Filter to the output
- Export
However, in your specific case, you can not do step #2 because your file has captions, not subtitles. So you would need to extra steps to convert the captions to subtitles in an external application.