Is it safe to run jobs during production hours?

Yes - but also depends if you are making changes such as Broken Link Find/Replace or List Settings changes.

You may not want to do live changes if you need time to validate the changes on your production environment.

The jobs will run and use server resources but it will be very similar to users accessing the website and the server responding to those requests. The difference is the tool will be accessing the web front end server to get information very frequently, so you should monitor the server resources to see how the web server handles these requests.

Normally the utilization is minimal and the web server will maange these requests accordingly. The tool works similar to a SharePoint timer job that will access and retrieve information in the background. The tool uses the SharePoint API/web services to connect and get information - so it is safe and the recommended way to do this by Microsoft.