This is not a logical or acceptable solution.  What you are suggesting is to test a process which if it fails would be the process we would have to use to restore or original data. Clearly that is a logical fallacy. 

As you clearly stated in your suggestion, the backup and restore process does not restore everything. That means by doing our "test in production", if the test fails we would not be able to restore those items which are not backed up and restored.

Obviously, this is not a solution.