4K monitor load on RTX-3090 during renders?

I’ve read through a few older threads on using a second dedicated GPU to drive your PC’s displays, leaving the more powerful GPU dedicated to rendering. I’m wondering though how much of a load that a 4K monitor impacts the rendering capacity of an RTX-3090? My main production machine is not used for multitasking during renders, so I’m only concerned about the “background” monitor load on the machine while it’s rendering. I’m using a 4K monitor as my primary display with a smaller 1920x1080 as the secondary display.

Is it worth installing a second GPU to drive the monitors, or is the monitor load on the 3090 negligible enough to make this pointless? I have my old GTX-970 that I can dedicate to the displays, though I’d prefer to not have to deal with reconfiguring my PC case/PSU/airflow setup to do that if it’s not going to bring about a worthwhile improvement.