I am going to purchase the 3080. I was wondering if it was possible to put the 3080 in the primary PCI-E slot and bump my 1060 down into the secondary one and have it dedicated to streaming. Like put the setting to NVENC and have it all run thru the 1060. I am trying to cut corners in spending. My more tech savvy friends are saying I need to get a new CPU to keep up with the 3080. For context I have the Ryzen 5 3600.
If you are playing on 1080p your more tech savy friends are right, it will bottleneck the 3080 for sure, If you are playing on higher res its worth trying. (However the 3070 is faster then the 2080ti and the 3600 MIGHT keep up with it at 1080p, especially if you can overclock)
The 20xx series was a major bump to NVENC, since then i see no reason to have a 2nd PC for streaming, The audio setup is a nightmare and 20xx series nvenc is the same as 264 (CPU) medium preset, which is a major leap forward, only the most expensive CPU's can run better presets
You will literally be using 2-4% CPU and 0% GPU usage with OBS
The short answer to your question is no, sell the card.
But it won't matter, even if you could use the 1060 as a dedicated streaming card it would cause more troubles then its worth just to save 2-4% CPU usage... This is with preview enabled and 1080p 60 fps stream quality. The 1060 uses different drivers then the 3070