Actually yes!
it's possible. I'm not sure if it's possible to do that for systems using an Nvidia GPU, but I've tested it on a system using an AMD GPU and it worked fine.
There is a way to run all your GPU demanding processes (like games or any other application that uses graphical rendering) through the GPU but still get the output from the VGA output on the motherboard.
specs of the system I've tested it with:
MB: Biostar mhv3
CPU: Intel Core i5 4460
GPU: Radeon RX 480 8G
RAM: 2X8GB DDR3 1600
Take these actions step by step and you might be lucky:
1- Backup all your files and get ready to install a fresh windows10 (2004 build preferred)
2- Remove your GPU from motherboard PCI slot and connect your cable directly to
the onboard VGA output of your motherboard
3- Go to BIOS settings by pressing 'Delete' repeatedly right after restarting, when you're
in BIOS settings screen, find Intel HD Graphics settings, (if you can't find it google
it) it's default state might be set to Auto or Disabled, change it's state to Always
Enabled. then save and exit.
4- Turn system off and plug your GPU back into the motherboard PCI slot but your cable
should still remain connected to the onboard VGA output. make sure that
the power cable (6 pin or 8 pin) remains unplugged from the GPU, don't worry it won't
get damaged. otherwise you might get a black screen which won't let you proceed to the
next steps.
5- Start installing windows10
6- When finished installing, install latest Intel HD graphics driver among with other
drivers for your chipset but not the GPU driver yet, then restart the system.
7- After restarting, log back into the windows and you see that Intel HD graphics is now
your primary display. now turn off system completely, then plug the power cable
into the GPU
8- Turn on system and install latest stable (not beta) version of AMD GPU driver knows as
AMD Radeon Software (version 20.4.2 preferred) or the latest NVIDIA GeForce Graphics
Driver (456.71 WHQL preferred).
9- If installation was successful, make a restart to finish installation of it. you should
now be able to fully utilize your GPU in
running games and other graphical processing apps while getting the output from your
onboard VGA without the need to use an adapter to use the output on GPU.
NOTE: I hope it works for you, it did work for me. but again, about Nvidia GPUs I'm not
sure if it works or not, you can test it yourself to find out.