No, not as far as Pi-hole's DNS services are concerned.
This setting only affects what the OS on the machine hosting your Pi-hole is using for DNS.
By omitting a DNS server in your static defintion in dhcpcd.conf
and moving DHCP to your Pi-hole, you'd probably press your Pi-hole host's OS into using a DNS server as learned via IPv6 NDP/RA.
This would not contribute to your observation, but may pose a separate issue if other clients would also receive that information, and thus be able to by-pass Pi-hole via IPv6.
Depending on which device that IPv6 address belongs to, this may or may not be an issue, abeit a separate one. That said, since you seem unaware of configuring one of your Pi-hole host's IPv6 addresses in your router, it seems very likely that IPv6 would belong to your router.
While this would have to be dealt with, it wouldn't contribute to your current issue at all: Pi-hole is completely ignorant of your network's DNS configuration.
(If Pi-hole would be using the same DNS resolver as your network (which should be Pi-hole, of course), then it would query itself in an infinite DNS loop.)
The important takeaway here is that Pi-hole's own DNS configuration is entirely independant from that of your other network clients. Pi-hole uses only the definitions form its own configuration, and specifically, it would use only those upstream DNS resolvers that it's configured for.
Changing it won't affect your original observation (which your examples tied to IPv4 anyway).
Depending on your ISP connection and the way your router handles disabling of IPv6, that may cut you from internet connectivity, e.g. if your ISP was IPv6 only or DSLite.
Could you elaborate on that?
It's not clear to me where you've put which address.