There is no distinction between the admin password failing and the user password failing. Some will want it others will complain that even indicating the password failed is too much info.
I was thinking of the following scenario before I posted this naive thing.
I am a customer, trying to debug why I am getting a "Password verification failed". I keep thinking that the bind to my userid DN is failing, when in fact the bind to the admin DN may be failing. That is loss of cycles.
No big deal.