When trying AMDGPU-PRO 17.10 as the latest driver paired with Ubuntu 17.04 stock, sure enough the install fails. The DKMS module doesn't build against Ubuntu 17.04's stock kernel based on Linux 4.10:
So next I decided to try falling back to Linux 4.9.0 from the Ubuntu Kernel Mainline PPA. The DKMS build succeeded, but when trying to load amdgpu, the amdkcl driver loaded and had an unknown symbol issue.
So then I fell back to Linux 4.8.0 from the Ubuntu Mainline Kernel PPA. Linux 4.8 is what's used by Ubuntu 16.10 and the Ubuntu 16.04.2 LTS HWE pack. Kernel-side everything was good, but Ubuntu 17.04 uses X.Org Server 1.19... Ubuntu 16.04.2 l / 16.10 rely upon X.Org Server 1.18.
AMDGPU-PRO ships its own X.Org packages for the AMDGPU DDX, Modesetting DDX, and GLAMOR EGL. With those being built for Ubuntu 16.04 that uses xorg-server 1.18, ABI breakage causes the display to fail.
But if removing AMDGPU-PRO's xserver* packages to instead default to Zesty's stock AMDGPU/GLAMOR (and still using the downgraded Linux 4.8 kernel)...
You can get the AMDGPU-PRO stack working, at least the basics.
Or for my purposes in wanting to get AMDGPU-PRO working on Ubuntu 17.04: for its OpenCL stack with Clover not being a viable option.
Hopefully it won't take AMD too long before they officially support Ubuntu 17.04, especially as it took them until earlier this month to properly support Ubuntu 16.10/16.04.2.