Surprisingly, it seems to work just fine. There's no official support for 2023.4 but I could both install a new VM and upgrade an existing VM from 2023.3. (I had to update Parallels Tools before I upgraded Kali to avoid kernel panics.) Running Parallels Desktop 19.1.1 on an ARM64 Macbook Pro.
You need to run the installer manually. I didn't have to change any configuration files or add manual kernel-headers like we're used to with new Kali releases on Parallels.