So, my answer in brief is: YES you ALWAYS want a CMA when making an offer on ANY property, bank-owned or not! It is a very important thing, but not for the bank's benefit; for yours! The bank won't care about your CMA, but you should.
As far as swaying the bank, producing things rarely sways them. What you will want to do is keep your offer and it's contingencies AS SIMPLE AS POSSIBLE. The cleaner the offer, the higher your chances. Beyond that, you just have to make it make sense to the bean counters. There's no trick to this, it's just the dollars and sense of it to them. Offer the dollars, show why it makes sense to them and, if they agree, you've bought yourself a house!
I think that if you put together numbers that reflect where your asking price stems from you are producing valuable information for the bank. That said, the bank, unless local, could care less. It is a numbers game to them and so at this point they need a certain number. When push comes to shove they will take the lowest number they can if there are no other offers on the table. I have dealt with a number of these this year. You really need someone on your side to procure the right property at a great price. Give me a call or e-mail me and we can get started. Unless of course you are working with someone. Thanks-Mark Gladue 239-5593 firstname.lastname@example.org