You can, but it disconnects it from the host, so you'll be headless. Which may be fine for a lot of people if you are able to ssh in and manage it that way.
This is exactly how I have mine set up aye. Proxmox on hardware, Main PC as a VM - once I got to the point where Proxmox had its web interface (and ssh) up and running I had no real reason to have a monitor plugged into the hardware OS anyway. Passed the GPU and all USB ports to the PC guest from there.
At the time I had no idea how popular it was to run this setup, I thought I was being all weird and experimental. Was surprised how smoothly everything ran (and still runs, a year and change later!)
Bonus, I was able to just move the PC to another disk when the SSD it was on was getting a bit full. Moved PC's storage onto a spinny HDD to make room to shuffle some other stuff around, then moved it to another SSD. Didn't even need to reboot the PC VM, haha.
Proxmox backup server running on my NAS handles deduplicated backups for it and other VMs too which is great.
But i'd be happy to be proven wrong.