If that was true that quicksync wouldn't work in any way with a third party card, without the monitor being connected to the intel adapter & the intel adapter being the primary render. Then please explain the following 3 examples.
1.
As you'll notice that here both drivers, hardware and feature programs are both loaded and working with the nvidia card as the primary adapter.
2. OBS Game Streaming Performance Boost with Intel Quicksync - YouTube
3. https://obsproject.com/forum/threads/intel-quick-sync-is-beautiful-and-the-future-of-streaming.7597/
& on top of that, in 2013 twitch announced a partnership with intel to optimize compatibility with quicksync. Considering twitch is for gamers, that announcement also suggests that people streaming using quicksync would be using a different primary adapter as the intel HD adapters wouldn't be powerful enough to run any 3D game at a respectable performance while doing x264 encoding.
I'd be more than happy to agree with you if it wasn't for the overwhelming evidence suggesting the opposite to be true.