most routers let you set a primary dns server and a secondary. just set the secondary to something like google or cloud flare dns.
If i understand you correctly, if you have a blocking internal DNS running pihole or Adguard and an external general DNS such as google or cloudflare, unless what you described can be configured, the requests that come back "blocked" from pihole would then simply be resolved by google/cloudflare, thus negating the point of pihole.