Question about MSI GeForce GTX 1080 GAMING X 8G

I have a special question, I hope I am summarising this correctly. I have an HP notebook that does not have 4k but only a full HD display. I would now like to have 4k resolution with an additional 2nd display (4k screen) for gaming. I have seen the video and therefore now this question. Could I play 4k games and also still have 4k resolution with an additional 4k screen? https://www.youtube.com/watch?v=3_y5j57_eOg I have seen that with an additional ''docking station'' (accelerator) (an external graphics card (GeForce GTX 1080 Gaming x 8G) and play 4k games) and can play 4k games: HP OMEN by HP Accelerator GA1 (External) The whole thing is connected to a Thunderbolt 3 port, which of course my notebook also has, of course. So, what I have understood now: I can play 4k games on my notebook 4k games smoothly on my notebook with this ''docking station'' without any stutters. Logically, I still don't have a 4k resolution in the display because display because my notebook ONLY has Full-HD. But this solves the first problem for the time being (judder) is solved. But now I would also like to have 4k resolution in the display. Now my main question: if I take an additional 4k screen and then connect it, will I also have 4k resolution on my additional 4k screen even though my notebook only has Full HD? I would like to buy this ''docking station'' (Accelerator) but but I am not sure if it works. It is still quite new on the market and you can't find much about it on the internet. Sorry for the question, I don't know much about it, I'm a beginner, otherwise I wouldn't ask, I'm very new in the gaming world. This is my first graphics card I'm buying. Other information about the notebook: HP Spectre x360 Intel® Core™ i7-7500U Working memory 16GB Processor clock speed up to 3.50GHz (with turbo) Graphics card HD Graphics 620 (Intel)