RE: Inspiron 15 Gaming 7567 HDMI Specs/Does HDMI out support full bandwidth for G-SYNC Dell Gaming Monitor – S2417DG
The NVIDIA rep is wrong about the signal being swapped between the two. Yes, the NVIDIA GPU will take over rendering duty, but the Intel GPU is always the one connected to the displays. And even on systems that can be configured to have the discrete GPU take direct control of the display outputs, that's something that has to be toggled in the BIOS, not something that happens dynamically.
What spec are you reading that says HDMI 2.0? If it's the specs of the NVIDIA GPU, don't rely on those for the reason I just mentioned. Again, I have not seen any Dell laptops yet that support HDMI 2.0.
So in terms of the display to buy, you may actually want to consider a display that has features your current PC won't use, on the very reasonable assumption that that you'll be keeping your new display longer than this specific PC, in which case you can make sure that the next PC you buy will be able to use those features. In that case though, I would suggest waiting for HDR displays to hit the market. ASUS has a 4K, HDR, G-Sync, 144 Hz display coming out early next year, which basically ticks all of the gaming boxes. The downside is that you'd have to use it as a 1440p, non-HDR, non-G-Sync, 60 Hz display today. That still wouldn't be a bad experience, though. The only potential issue is that a panel with a native 4K resolution being run at 1440p might have some blur, but then again given 4K's pixel density, maybe not. If you don't want to take that chance, you might still want to consider waiting at least for HDR, since that really will be a major improvement once you have a system that can use it. If you don't even want to do that, look for a 1440p display that's ideally IPS for image quality purposes and has a fast response time. ASUS makes some great gaming-oriented displays, for what it's worth, and there some good "Best gaming displays of 2017" review shootouts that should help you.