Will a second GPU on a second monitor improve gaming performance?

I like to watch sports or tv shows on my second monitor while I play video games on my main gaming monitor. I was wondering would I get better performance in my video games if I used a second GPU on my second monitor which in theory would off load my main GPU (1080TI) and potentially improve gaming performance. 

So I did some benchmarking to determine the answer. I did some performance measurements with my second monitor connected to my CPU's integrated Intel 630 graphics and with a second GTX 970 card installed. Then I streamed soccer and played Jumanji 2 in 4K on my second monitor while running benchmarks in Watch Dogs Legion, Forza Horizon 4 and Assassin's Creed Vahalla. Below are the results:

CPU: Intel i7-8700K @ 5GHz
GPUs: Nvidia GeForce GTX 1080 Ti, Nvidia GeForce GTX 970, Intel 630
Ram: 32 GB DDR4 @3200Hz, CAS 17
Gaming Monitor: 1440p Native Resolution @ 165Hz 
Second Monitor: 1440p Native Resolution @ 60Hz 

These results were not what I was expecting. I thought having a dedicated GPU powering my second monitor while watching sports or movies would greatly improve the FPS on my gaming PC but the difference was only one or two frames per second. 

The second surprise is I would get 9 to 16 frames per second less on my gaming benchmarks when using the Intel 630 or Nvidia 970 to power my second monitor while streaming soccer to it through DAZN. I noticed in that situation the CPU usage was much higher which was causing lower performance in the game.

It my tests, is it is not worth powering a second monitor with a less powerful, dedicated GPU with my configuration. If anything, it could potentially cause a noticeably worse performance. Streaming soccer or watching a 4k movie with both monitors connected to my 1080Ti had very little impact on the gaming performance as the difference was between 0 to 4 FPS.

UPDATE: by enabling Hardware Accelerated GPU Scheduling in Windows 10, the hashrate did not drop significantly while watching video like Youtube or streaming sports.

"Windows Settings > System > Display > link at the bottom of the page: "Graphics Settings". Enable Hardware-Accelerated GPU Scheduling