No, it will not.
You should not. Any DNS server available to clients is liable to be used at any time, resulting in DNS traffic bypassing Pi-hole.
One way to increase reliability (if you have problems keeping your Pi-hole running) is to add a second instance of Pi-hole on a different device or on a device that is already running 24/7 (a NAS, for example).
Then you would enter the IP's for each Pi-hole in the DHCP settings on your router. If either Pi-hole fails, the other continues serving the entire network with no network downtime.