AMD funded a drop-in CUDA implementation built on ROCm: It's now open-source

You probably can, but why would you? The main (only?) reason to ignore the CUDA-based stack is so that you could save a bit of money by using some other hardware instead of nVidia. So the amount of engineering labor/costs you should be willing to accept is directly tied to how much hardware you intend to buy or rent and what % discount, if any, the alternative hardware enables compared to nVidia.

So if you'd want to ignore CUDA+PyTorch and reimplement all of what you need on top of Vulkan.... well, that becomes worthy of discussion only if you expect to spend a lot on hardware, if you really consider that savings on hardware can recoup many engineer-years of costs - otherwise it's more effective to just go with the flow.