No you can't initiate a backup remotely, but you could log into iCloud on another device or a computer and look to see when the last iCloud backup of that device was completed to know what might be lost if you erase it.
Also look in iTunes under the preferences for devices to see if you have a local backup of the device as well.
On the iCloud preference pane for Mac, you can press the manage button next to the storage graph at the bottom of the window and inspect the date/time of the last backup for each device you have established.
