nixos is already, from a certain perspective, an exotic take on gentoo. take away cache.nixos.org and it becomes a source-based distro. it's not even too out-of-the-question to do traditionally gentoo stuff like globally set -funroll-loops -O3 and rebuild your whole system, but the operational benefit of staying standard is getting to use binary caches since reproducibility lets them substitute transparently for local builds in the standard environment with the standard settings. one thing nixos lacks is an elegant analogue to gentoo USE flags; "tell package A to use optional package B" has like two different conventions in nixpkgs for individual packages, alongside bespoke things like configuring everything to use cuda or not. furthermore, pkgsrc, gentoo prefix, and nix are three of a kind in terms of "third-party package manager on a non-native OS"
personally, i used gentoo throughout most of my teenage years, and now use nixos viewing it as a successor, since you can screw around using the thing as a meta-distribution, but roll back when you hose your system.
gentoo freebsd existed for a while for funsies but nobody cared and now it's dead, same with gentoo openbsd. each was portage integrated a little more intentionally on top of a respective bsd than just "bung it in /usr/local/bin and call it a day". practically speaking, they were implementations of gnu/k*bsd.
nixbsd similarly exists (nix deeply integrated into freebsd), with heroic efforts made to transfer nixos's abstraction over init systems for system-wide configuration; last commit was two months ago so i guess not dead yet?
you can run nix on gentoo, or gentoo prefix on nixos with nix-ld turned on if you feel like it
void's claim to fame with xbps is a bunch of sandboxing and bind mounts for build environments. nix already has to sandbox just to get off the ground wrt reproducibility.
void, gentoo, and nixos all offer some degree of libc freedom. on void it's first-class, on gentoo it nearly is, and on nixos it's here be dragons. libc freedom doesnt really jive with using a bsd as a base; vertical integration is kind of one of the contemporary selling points.
so to answer your question, the result would be nixbsd in an alternate timeline where nixpkgs's analogues to USE flags/eselect/profiles are not hot garbage (i say this with love as a user), and void would fail to exert a phenotype.