NPSP - Recurring Donation Mapping Behavior

What is the expected mapping behavior of custom Recurring Donation fields to Opportunities when installment auto-creation is disabled

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For example, I want to map a custom 'Acknowledgment Status' field on the Recurring Donation to the 'Acknowledgment Status' field on Opportunities. If NPSP were set to auto-create the next installment, the Recurring Donation's Acknowledgment Status would get mapped to the new Opportunity. However, we have installment auto-creation disabled. So if the next won installment for a Recurring Donation comes in, say, through an online donation platform, would its Acknowledgment Status be inherited from the Recurring Donation:

• When it's created?
• In a batch overnight?
• At all?
• And would the Recurring Donation's Acknowledgment Status get copied to all child Opportunities, or just new ones after the field is updated?

Thank you for any insight you can provide!