The bank I used to work at logged mail in this manner, using the same log they used for the night deposit. One log page per day per branch, listing all transactions received in any method other than in person. I am not aware of an auditor ever asking to see it, however there was a time or 2 we used it when a customer was insistent that their deposit was mailed to us and we didn't process it, or that we didn't process it the day we got it (supposedly!). The fact that we had a dual control list of what was received every day was useful in those occasional situations.
That bank, though, was a very small community bank (<500m). There, the occasional benefit was sufficient to justify any time expenditure that the process caused.