Yes, if you'd opt for having your router distribute its own IP as local DNS server, and having your router use Pi-hole as its upstream DNS resolver.
You'd then just need to change your router's upstreams to instantly by-pass Pi-hole for all of your network.
This comes with a couple of potential drawbacks:
In such a scenario, your router will become Pi-hole's only client: Since all DNS requests received by Pi-hole originate from your router, you won't be able to attribute DNS requests to individual clients anymore, and consequently, you wouldn't be able to apply client-specific filtering.
You'd also have to be careful about avoiding a DNS loop, e.g. by enabling Pi-hole's Conditional Forwarding (which would be useless in that scenario anyway, as all requests are from your router's IP).
All of the above would affect your entire network, including your non-static clients.
I guess you could try to hand out your router's IP as local DNS resolver only for your static-IP clients - provided your router would support that, and if your static clients would be identifiable by your router.
But I'd expect that to be available mainly (only?) with custom ROMs on your router.
If Pi-hole would be your DHCP server, you could address this via a custom dnsmasq configuration (but you'd still have to be cautious about aforementioned DNS loops).
Things you can do with dnsmasq! is an older post, but it should still largely apply:
Of course, you'd have to adopt that to distribute your router's IP instead of OpenDNS and Google.