The PyTorch conda binaries and pip wheels ship with the specified CUDA (cudnn, NCCL) runtimes, not with a complete CUDA toolkit.
To run PyTorch you would thus not need a local installation of these libraries and could use the binaries directly.
However, if you want to build PyTorch from source, any custom PyTorch extension, or any other CUDA code, you would need to install the CUDA toolkit on your machine.