Is there a way to do this?
Yes, you can get notifications based on category, tag, or a specific topic. See:
So the help explains
Don’t worry about missing a reply – you’ll be emailed any notifications that arrive when you are away.
How long does it take to get that email?
The default is to wait 10 minutes before sending any notification emails, to give users a chance to edit and finalize their posts.
This number can be set to any value by an admin using the email time window mins site setting.