Are there any 3rd party repos for NixOS?

Define "repository". For most definitions of a repository the answer would technically be "yes" but yours might differ.

Would it be possible, for propietary software compiled directly for NixOS, to have a binary-only (as opposed to source, or binary+patched) repository?

No. For a "native" Nix output path, you must have the full build definitions; Nix expressions.

In the case of most proprietary software in Nixpkgs, the BLOB of the actual thing is a FOD (fixed-output-derivation) which obfuscates everything behind it; meaning it can't depend on other Nix output paths. Only the the dependency DAG for the wrapping around it is known.

Let’s say I want to add some extra, propietary codecs unavailable to NixOS. How would I be able to change a dependency so that each package dependent on it automatically picked it?

This is what overlays are for. They allow you to change the meaning of some package name in the context of an entire package set in which other packages may depend on the meaning of that package name. Those packages will have the change in meaning propagated to them.

Note that changing a low-level package with many dependants such as i.e. mesa will cause a change in those dependants derivations; a change that is not present in the expression used for the central binary cache and therefore requires you to build the packages yourself. With a decently fast computer, building a typical desktop closure from such a low point onwards will take at least half a day.

Are there any 3rd party repos?

Nix has "flakes", which allow you to share Nix code in a Git repository, it's like repos on steroids. There are many Git projects that offer new packages (such as nix-gaming) or NixOS modules (such as my project nixos-router), or even just Nix code (such as my projects notlua and notnft, which allow you to write Lua code and nftables rules in Nix), or any combination thereof.

Would it be possible [for proprietary software to be compiled for NixOS]?

Kind of. You first have to understand what Nix derivations are - builders that take certain inputs (such as certain versions of libraries) and produce some outputs.

What happens if the inputs (such as a library version) change? The outputs change as well - previously it was /nix/store/abcdefgh-libfoo/lib/libfoo.so, now it's /nix/store/ijklmnop-libfoo/lib/libfoo.so - the path to libfoo changes, and the binary's RPATH reflects that.

So if you want to package binary software for NixOS, you either have to pin library versions (so the paths don't ever change), or patch the binary.

...proprietary codecs...

It depends on what those codecs are.

Let's say they are a binary. In that case, you install them and they get added to your PATH - easy.

Let's say they are some data files. In that case you install it and it gets put into XDG_DATA_DIRS - easy.

Let's say it's a shared library (.so). First question - how is that .so loaded? By which program? From where?

Depending on the answer, what you have to do changes as well. You may have to override some core media library, or ffmpeg, or maybe you can override VLC, or VLC's ffmpeg, but not system ffmpeg. Or, it may be the case that a simple LD_LIBRARY_PATH change will do it for you.

Basically - it depends. That's why NixOS requires a deeper knowledge of Linux, or forces you to learn.