There is actually two questions here :
Do I need a dedicated GPU in my server ?
It depends on your needs. Dedicated GPU on servers are used for highly parallelized application (number crunching, physics simulations, signal processing, AI, cryptomining, etc.). If your applications relies on CPU only you don't need any dedicated GPU.
Do I need a video output on my headless server ?
Yes, yes you do. While it's technically possible to have a server running without it, it's very convenient to be able to plug a monitor for maintenance purpose (OS install, BIOS update, diagnostic, etc.). This video output on a server is provided by a very light integrated GPU or an management interface. I don't recommend relying on a graphics card lying around to get video output from the server, the last thing you want to do when you server is unresponsive is to have to shut it off and switch hardware to diagnose the issue. You should have a readily available way of getting video & keyboard access, IPMI is great for that but an integrated video output can also be a life saver in last resort.
Most recent server motherboard comes with a dedicated chip for platform management and basic video output, you should use it or at least get used to it for the day you'll need it.