Question Can I use the M.2 slot to connect an external graphics card?

I would be very about doing that.

Have you been able to read the applicable installation/user manual for the adapter? Including all fine print and caveats?

Update your post to include full system specs and OS information.

Include PSU: make, model, wattage, condition (original to build, new, refurbished, used).

History of heavy gaming use?

Look at the voltages being being used. And map out pin/voltage connections. M.2 requirements and GPU requirements.

What is driving the requirment for an additional graphics card?

What GPU are you planning to use?

Why external? Is there a particular problem?

There may be other solutions but more needs to be known.
 
For now I'm just exploring options.
The laptop only has an integrated Intel® HD Graphics 520 graphics card. I would like to play some games now and then, so I would like to connect a slightly more powerful graphics card. I chose the NVIDIA GT 1030 because it has low power consumption (about 30W) and quite acceptable performance for my purposes.
I would like to fully integrate the graphics card into the laptop (into the space instead of the DVD drive).
I would solve the power supply, +5V and +12V, using a step-down DC-DC converter. I don't have the laptop at home yet, it's on the way, it's a Getac S410. There could have been an add-on GTX 960 graphics card as an option, but it's unavailable, so I decided to go that way. I was also thinking of using the ready add-in card connector and trying to connect the NVIDIA GeForce MX150 GPU - 2GB VRAM WDJ8P - from the Dell Inspiron 7773. Of course I would have to know the wiring of the contacts.
 
Thank you to everyone involved for their opinions and comments.
So I found out that this is not the way to go, the performance loss when using the mini Pci-e is approximately 30% when using the laptop's internal display 🙁
So I'll try plan B.