The proposed setup in the following is most probably not best practice, but will it work?
Background/motivation
We have recently upgraded all the laptops in our household, both work machines and private and I have realized that they all have TB3 ports. So I want to make our shared family PC desk modular with a TB3 dock so that we quickly can switch between machines at the dual (hopefully triple soon) screen setup with printer and other peripherals. The idea is of course that we just need to plug/unplug a single cable.
Up until now we have used my elderly desktop PC (connected directly to screens and peripherals) with a multi user setup. I want to still be able to connect the desktop to the setup, and I would like this to be easy (i.e. single cable).
Question
Is it possible to use a USB-C PCIe card to connect the desktop PC to a docking station and still get a decent graphics performance in a multi display setup?
Will the USB-C port even be able to carry a graphics signal? And if so will the system use the graphics card or the integrated graphics in the CPU?
Bonus questions
If this is the wrong way to do it, is there another way to achieve the above that does not require a big investment (the PCIe card is cheap)?
Would it for example work if I instead of adding the PCIe card replaced the graphics card with a newer model with a native USB-C port?
Details
I consider acquiring this hardware setup:
Dock: https://i-tec.cz/en/produkt/c31tripledockpd-2/
PCIe card: https://www.asus.com/dk/Motherboard-Accessories/USB_31_TYPEC_CARD/
My existing desktop machine:
CPU: i5 2500
Graphics: GTX660