Why would it? The PiHole would be on your local network, so it would never need to go past your router. So the request itself would be private, what matters is what you do with the response. Theoretically, the PiHole would only give responses for things it’ll block (usually directing it to localhost or something), and have no response for everything else (check your configs).
So if you get a response from the PiHole, you route the request locally, which does nothing. If you don’t get one, you’ll check the secondary DNS, which is provided by the VPN service.
You should certainly confirm this before completely trusting it, but it should work fine.
Yeah, I might end up getting one for that. My current TV doesn’t have ads, but does have enough smart features to have a Jellyfin app, so I’m good for now. But my SO wants a bigger TV, so that may end up being sooner than later.