Yes.
I'm working to gather data to indicate whether or not this is the case, but prefetching at the Pi-hole level could actually trigger additional prefetching (in a good way) at the Unbound level - based on the publicly shared Unbound prefetching algorithm. This assumes Pi-hole's algorithm functionally mimics Unbound's, and caching is done at the Pi-hole. If Pi-hole's algorithm differs from Unbound's, in a complementary fashion, it's possible that it could further increase the overall cached response rate.
Additionally, you highlighted the other obvious benefit - non-Unbound users would be able to capitalize on a DNS prefetching on their Pi-hole.
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Does your network only see one query per hour? If not, better cache return ratios are likely to be more frequent than hourly... See Bucking_Horn's math below your comment for an estimate on the impact to the average user. I'm still gathering my own statistics, but using an existing post from sawsanders as a reference, he had 13137 recursive look-ups in a 6-day period, or ~90 recursive look-ups per hour (assuming they were evenly distributed over a 24 hour period, and not preferentially happening during hours where people are actually using the network). For me, at least, an unbound recursive look-up takes somewhere between 100 and 1000 ms. Anything done to reduce the number of recursive lookup responses in a day is beneficial. A 1s lookup has a noticeable impact on page loading.
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Yes, the "con" to every feature request is that it will require development. That's the basic premise of a feature request. The beautiful thing is that once the basic prefetching code is in place, algorithms can be tuned to optimize prefetching over time. The system can start with a basic pre-fetching system like either or both of the algorithms I suggested in my first post, but over time can evolve. This is very much not the scope of the request today, but if a feature like this were to be implemented and allowed to evolve over time, prefetching would be a perfect candidate for a machine learning algorithm - they're designed for pattern recognition and prediction.