You do not need a card just for video output. The RX580 can mine and output video with no issues.
It depends what motherboard you have. Some old boards like the ASRock BTC pro, if you got all newer RX series
Cards, the system won't boot without a monitor plugged in or the fake HDMI emulator adaptor.
I even tried to enable or disable the onboard video and the result was the same. Without something plugged in to at least one of the GPUs the system won't even post.
Another way to handle it is if you got an old Pitcairn or Tahiti GPU, you can put that one in the main 16x and it should boot without a Monitor plugged into any of them.