Yep!
Someone asked something similar to this a few days ago:
You’ve asked specifically about doing it with a webhook. So that would mean, instead of retrieving the comments via the endpoint I mentioned in that other thread, you would set a webhook on the project(s) you want to do this in (you’ll need a separate webhook for each project), and monitor the data sent from that webhook for story added events. When you receive a new story you want to add as a status update, add it via the endpoint I mentioned in the other thread.
Please follow up if you have any questions about the above info.