That M.2 adapter looks like the kind that should work. Though no guarantees.
So the VIM 3/ 3L have the ability to be powered without using the uSB type-c port. The vin port on the board is what you would use for this It’s input voltage range is from 5v -20v. Since your wanting to add an adapter card with your VIM 3/ 3L. I would recommend using this port to power the board and your add-on card along with any drives, potential GPU’s, etc…So you shoudl get an AT or ATX power supply and use that to power all you devices. You’ll want to look on the internet for how to create and ATX bench power supply. Since your not likely to use anywhere near the power that the power supply can put out you can pretty much get any supply that is going to do 200W even if you plan on using a low end GPU. Something like this is the easy way to do it 24 pin ATX bench powersupply adapter
You can do this without that adapter. The lazy way is a having a power supply with a power switch and place a jumper wire onthe green wire ont he atx power supply to any black grounding pin. I generally use the 4/ 8 pin CPU power cable for powering the boards that I can with 12V as it’s already wireed for 12v and any modern supply will have this on it and using an adapter to the port and soldering the wires make it replace for when the power supply dies.
Your card should also plug the rest of the cable from the power supply as need for your devices. I find this easier but I’d just look around and see what you think will work for you just remember for powering things their is no real correct answers as long as you are supplying the right voltages and current needs of your devices.
The other thing to remember as well is that the m.2 slot is only PCIe 2.0 just keep that in mind with expectations of performance.