Sorry, let me clarify one of the statements earlier.

If you are using the Retrieval method of sending invoices, credit notes and payments from OE to AR, then separate Invoice and Cash batches are sent to AR. If you are using the Direct batch method, then only an Invoice batch is created, with payments attached to the invoice. You likely have the Direct method set up in OE, which is why you didn't see a Cash batch. Make sure of how your client is set up and if that meets the desired need.

Order Entry does not upate any bank GL accounts when posting - that is handled entirely by AR.