CUDA.jl installs all of the CUDA drivers and associated libraries like cudnn for you if you don't have them. Those are all vendered via the Yggdrasil system so that users don't have to deal with it.
CUDA.jl does not install the actual kernel driver, right? I do not really see how it can do that and the sibling comment does confirm that the kernel driver is not managed by Julia.
Yes, you would still need to the NVIDIA kernel driver (preferably the most current one). Desktop users typically have it already installed. But the main difficulty in my opinion is to install CUDA (with CuDNN,...). Even the TensorFlow documentation [0] is outdated in this regards as it covers only Ubuntu 18.04.
The installation process of CUDA.jl is really quite good and reliable. Per default it downloads it own version of CUDA and CuDNN, or you can use a system-wide CUDA installation by setting some environment variables [1].
