I was wondering exactly the same and then I was been able to achieve both setups. I should document it sometime. I used this guide successfully.
Since I have an NVIDIA graphics card and I picked Linux distributions that would come pre-installed with the proprietary nvidia drivers out of the box. (I may explore the open source version in the future, but I hear it’s not yet ready for prime time and I just wanted to get something working).
With Manjaro HVM
With Manjaro I could get everything working with the Qubes integration and the graphics card worked perfectly. The only thing is that the screen outputs from the graphics card to a second monitor.
When booting from the ISO, I selected the “boot with proprietary drivers” option and it booted right away on the second monitor.
If I install the qubes-gui package it’ll still display in the second monitor but the screen is white on the background. This hints me that the Qubes-gui is partially working but it can’t forward it to the original VM.
But at least here the graphics card is working perfectly fine, and blender renders work perfect.
Nobara
Nobara is a fedora-based “gaming”-oriented OS. I couldn’t really find its full source code and it seems to be a hobby project, but I gave it a shot anyway. And it worked (almost flawlessly).
As opposed to Manjaro, here the installer showed up on the main screen (the one coming out of the motherboard). Then after the installation, the “welcome screen” had options to install Nvidia proprietary drivers. After it installed the drivers, both screens showed the screen. After restart it only displayed output from the graphics card screen and the main one was black.
From there I could use it just like manjaro on the second screen, but then I tried integrating it with the qubes tools and here the GUI actually worked and it started showing blender, for example in its own window.
But it wasn’t perfect. Even though blender detected and used the graphics card, the UI was pretty slow. Other programs also detected the graphics card but had other issues.