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.