Pretty much. Not sure how the router determines which DNS to use, but mine seems to latch onto whichever one serves up results the fastest, which would inevitably be cloudflare direct after the pihole returns enough blocks.
So I use a Raspberry Pi Zero W as a dedicated pihole, and my Pi 4 seedbox acts as its own pihole and as a redundant backup. Then use gravity-sync from the Zero to the 4 to mirror the settings.
Except that, as I’ve already mentioned, I have two piholes, and sometimes both will be receiving requests. Based on your description, the second would never receive requests as long as the first is online. Perhaps this is router dependent, but it’s what I’ve observed.