Yes, I guess substituting the DHCP server behind the very same IP address should work, as long as the two won't fight over a common leases file (they can't here, because Pi-hole is isolated into its own container).
Of course, when a client requests renewal from Pi-hole for a lease that has beend handed out by your router before, Pi-hole wouldn't know that lease and thus could only deny that request, which should result in your client broadcasting for a nedw lease at some stage. May take a bit longer, but still should work.
Any progress on this?
The following may help you troubleshooting:
Create a custom configuration file for dnsmasq at /etc/dnsmasq.d/42-log-dhcp.conf (given your volumes, that would be /etc/pihole/pihole/dnsmasq.d/42-log-dhcp.conf on your host) containing the following line:
log-dhcp
To activate that option, run the following command from inside your container
pihole restartdns
This would allow you to see more verbose DHCP related messages, e.g. by running (also from a shell inside your container):
tail -n 10 -F /var/log/pihole.log | grep dhcp
You could use the following command to trigger some DHCP activity (from your host system this time).
sudo nmap -e eth0 --script broadcast-dhcp-discover
You may have to install nmap on your host system first if that's not already present.
Note that nmap may also pick up an answer from any other active DHCP server in your network.
Have a look at Reliably detect all DHCP servers on a network? - #8 by DL6ER if you suspect that a stray DHCP server would interfere somehow.