I'd be surprised if emulated performance were good enough, so it probably won't be usable until there's a native build. I also have no idea whether there have been any official discussions about that (and indeed, I was actually looking for the answer to that question when I stumbled onto this thread).
I'm going to give a gut feeling based on my limited knowledge of the code base and limited understanding of what Apple is shipping. Other folks can feel free to correct me if I'm wrong.
Given that OBS runs on ARM hardware already (folks have run it on Windows for ARM64 and on RPi), I would not expect any huge technical hurdles. The main pain point will probably be getting official macos-arm64 builds of the libraries that OBS depends on, then convincing somebody who owns the hardware to do the work to build it and test it.
Thankfully, Apple did (reportedly) make native OpenGL library support available on ARM (at least for now), so there's one huge bullet dodged. And folks got Qt building on Mac ARM silicon way back in July, which is the one dependency that I was most worried about, given how much more tightly it integrates with the OS than low-level bits like ffmpeg, x264, etc. The other dependencies will probably "just work".
One other likely headache is that (unless NewTek has released a new drop of their SDK in the last couple of weeks) the NDI library and runtime that a large number of OBS users depend on isn't available for ARM-based macOS yet. I don't know if linking against the static iOS binary is feasible (with some linker path rewriting) or not; it depends on whether that library links against any symbols that aren't available on macOS. I'll drop NewTek a line and see if they have any news to share on that front.
But mainly, I suspect it's just a matter of somebody having the right hardware and spending whatever time it takes to fix whatever any of the random build issues that invariably come up when you port a large piece of software to a new architecture/platform combination, and maybe adding a build script to lipo the x86 and arm64 app bundles together so that they can ship a single app that runs on both architectures.