Yes. It is your DNS server (and should be the only one). There would be no difference if you reboot your router or modem - you lose part of the internet path and lose internet during that time.
Providing other DNS servers in the DHCP process allows queries to bypass Pi-hole.
You have a few options:
(1) Setup Pi-hole on an independent device that won't be rebooted. Keep it running 24/7.
(2) Add a second Pi-hole, running in parallel with the first. Advertise both those DNS servers in the DHCP process. If you reboot the first one with other things running on it, traffic will seamlessly shift to the running Pi-hole.