Restoring an ADB backup onto a different phone of the same model? We have several Android 4.0 phones of the same model, from the same manufacturer, purchased at the same time, from the same factory batch. We have created a backup of one of the phones using ADB.

Can the backup file from one of these phones be applied to all of the phones, or is there uniquely identifying information in the backup that will make it inapplicable to the other phones?
The backups created from adb have no "checks" to see if the phone you are restoring to is the same device. 

You should have no issues as long as they are the same version of android. By same version I mean the same actual android version as well as the same manufacturer. You would probably have issues if you tried to restore a backup made from a sony phone with android 4.1 to a motorola phone with 4.1. But should be ok if you restore from a motorola with 4.1 to another motorla phone with 4.1.

You mentioned that you are going to the exact same device, just make sure the device is updated to the same version that your old phone was.