I've done both ways. I have an AMD video card so I thought I might as well use and leave the Nvidia dedicated to Deep Stack. But before that, I drove my monitor and DS off the same GPU with no noticeable slowdowns or stability issues. One thing I would not try is using an NVidia GPU for Deep Stack and encoding/reencoding as it will starve DS to the point you will get AI has timed out errors. At least I did with my low-end GTX 1060 with only 3GB of memory. Use Intel hardware acceleration if your CPU supports it, otherwise just stick with a regular CPU.
I used a GTX970 for DS and video for quite a while with no noticeable delay in either. Now I'm using Intel for video, new mobo with onboard video. No significant change with DS detection times.