Hello!
This might not be the right community but I'm looking at building a new server and you operate in similar areas and might have experience with this.
I've got a GPU without video outputs, can I combine that with a CPU without integrated graphics and still get video output from the HDMI located on the motherboard?
No. The video card is only wired to send video out through it's ports (which don't exist) and the ports on the motherboard are wired to go to the nonexistent iGPU on the CPU.
In windows you're not sending the signal directly through another port. You're sending the dGPU's signal through the iGPU to get to the port.
On a laptop with nvidia optimus or AMD's equivalent you can see the increased iGPU usage even though the dGPU is doing the heavy lifting. it's about 30% usage on my 11th gen i9's iGPU routing the 3080s video out to my 4k display.