That said, again, dishwasher detergent is basic, so you’re right in that adding acid probably won’t improve the efficacy of the wash cycle.

Though I can’t confirm this, I suspect that the vinegar is mostly removed with the the pre-rinse water, which may negate or disrupt an added pre-rinse detergent, but should be mostly gone by the main wash to not effect the main load of detergent released at that time.