I think it might be worthwhile to repeat what information category 2 banks exchange in detail and how they exchange it at this stage.

U.S. taxpayers resolving their U.S. tax consequences by OVDP, streamlined (by transition or otherwise) or still otherwise might be better off to advise the Swiss Category 2 banks if they have been less than truthful in their resolution of the U.S. tax consequences.
Category 2 banks are sending over account numbers (without names), balances and transactions to DOJ. They divide them in a "red flag" list which they pay penalties on and a "green light" list which they don't pay penalties on because the account holder is already in compliance or have joined the OVDP (and provided proof to the bank). The information is the same at this stage, except that the "green flag" list include some form of evidence of the requirements, such as a copy of the OVDP acceptance letter. The bank has to receive this from the client, as well as consent to share this info with the DOJ, otherwise they would commit a Swiss banking law crime at this stage.
Its fair to assume that the "red flag" list will be subject to John Doe requests already being prepared and that more detailed information such as communication between bank and client, account opening papers etc might be included in the John Doe summary.
One critical issue is if there will be a John Doe request on the "green light" list. I guess it could be possible but would they spend all that resources? And would the Swiss agree to this since it is a huge workload considering the banks are bending backwards already?
From what I understand at the heart of the deal was what info could be shared (without consent from the client) and that is after all fairly limited. I assume that all clients who are cooperating with the bank are smart enough not to sign a blank POA for the bank to give IRS anything but the specific limited information they need to prove their entry into OVDP.
If you have joined the OVDP (or streamlined), you have given proof of this to your bank of this so that they have put you on the "green light" list. As long as you don't lie in your OVDP documentation about basic things like account numbers, balances or transactions (which would be beyond stupid), I have a hard time seeing any other information being shared automatically?
The only way the DOJ could later get more information on the account would to pressure the client to hand it over within the ODVP process, or, if the balances or account numbers do not add up, use that as an indication of fraud and make a treaty request for that specific account. But again, it is really only things like account numbers, balances and transactions that could be subject to scrutiny here from what I understand and that I assume almost everyone hands over that same data in the OVDP or streamlined process in any case.
One conclusion from all of this is that it actually might make a lot of sense to cooperate with your category 2 bank in order to end up on the green list (if it is not too late already). Thereby you control/are aware of the bulk of the information being handed over assuming I am right about the future John Doe requests.