Don't do this. There is no reliable concept of "backup". Given multiple DNS servers, clients are free to use any of them, which will lead to some DNS traffic bypassing Pi-hole.
How is Pi-hole aware of this domain name mapping to a local IP? Typically this is done in a local hosts file entry or by using Local DNS records in Pi-hole admin GUI. Example from my network (the commands are run from the Pi, but the answer is the same regardless of which client makes the dig request).
cat /etc/hosts
127.0.0.1 localhost nanopi-neo
::1 localhost nanopi ip6-localhost ip6-loopback
fe00::0 ip6-localnet
ff00::0 ip6-mcastprefix
ff02::1 ip6-allnodes
ff02::2 ip6-allrouters
127.0.1.1 NanoPi
192.168.0.1 Airport-Extreme-3TB
192.168.0.2 TC-Extreme-3TB-extender
192.168.0.90 Sonos-Beam
From any connected client, the answer is as follows:
dig sonos-beam +short
192.168.0.90