Hi Claire,
> Approximately how long does the process take to backup a server site?
I don't believe there is a "good" accurate answer. The time will depend on the number of web services in your Server site, the complexity of the site (e.g., single machine vs. multi-machine), if high availability is enabled, your network configurations, etc.
> Can it be run while the server is in use without negatively impacting ArcGIS Server performance?
I would not recommend this. It's not a good idea to be making active changes to your Server site - while at the same time trying to back-up its configuration. A better approach would be to back-up the site in the evenings, when the site is not in use.
Back up and restore your ArcGIS Server site configuration—ArcGIS Server Administration (Windows) | A...
Hope this helps,
