Can a PC run a Minecraft server without a GPU?

You could give it a shot! I mean, if it doesn’t work, you can always try plugging in a cheap old GPU that you have lying around. A basic card from a previous generation should do the trick without breaking the bank.

Unfortunately, it won't work without a GPU. Consumer motherboards typically require one to get past the BIOS check. If you could manage to find a very inexpensive device that connects to HDMI or DisplayPort and tricks the system into thinking a monitor is attached, that might help.

To get around this, think about using a server motherboard instead if you're serious about running it headless. You might also consider installing Proxmox to manage your server easily without much hassle. That way, you can monitor everything remotely without interacting with the physical setup.

Most likely, you won't get past the boot sequence without a GPU on AM3 boards since they check for it right away. If you're just focusing on running the server, any old GPU should suffice. You could use something like a GTX 950 in your case if you want to run it 24/7 to save power—good choice!