I can reassure you that it does not encroach on anything the “host” distro package manager does and does not cause conflicts with it.
At runtime, it only ever touches things in `/nix; it’s self-contained.
The only time Nix needs to interact with the host distro in any way is during install where it must place a little glue in your system configuration for things like PATH, bash completions or the nix-daemon to work as expected.