I experience this also - if I'm doing a longer session of endurance work, the more I'm likely to see high HRV scores the next day. I see this in a number of my athletes as well.
I believe the more parasympathetic dominant you become, the more you'll see this with a corresponding drop in heart rate the next day.
Yes, it definitely can speed recovery and parasympathetic reactivation.
I generally see a drop in HRV after training. However sometimes I'm surprised by an uptick. On several occasions now, I've seen an uptick after 90 minutes or so of endurance type work either running or skating/cycling. In at least two recent cases, these 90 minute sessions were at my limit of performance. As an HRV user how would you explain this to yourself?