Answer
Yes, performing a backup of ArcGIS for Server while it is online is possible, however administrative changes to the site cannot be made when the backup is in progress.
There are two ways to perform a backup on ArcGIS for Server:
• Via ArcGIS for Server Backup Utility
• Via the ArcGIS for Server Admin endpoint
1. Log into the ArcGIS for Server Administrator Directory with the Primary Site Administrator (PSA) account.
ArcGIS for Server Administrator Directory default URL:
http://server.domain.com:6080/arcgis/admin
2. Click the 'exportSite' link.
3. Enter a destination for the backup file. If left blank, the .agssite file is saved in a temporary location with the path shown once the backup is complete.
4. Click the Export button.
Note:
Expect a brief downtime of services when performing a backup of ArcGIS for Server 10.1 and prior.