You could probably get it to do what you want, but it will be rather limited.
I don't know the size or power rating of the potentiometer, but you should never overload any part of a potentiometer. Many potentiometers are rated as low as 50 mW, some as low as 10 mW. Have a look at these:-
https://uk.farnell.com/webapp/wcs/s...ze=25&showResults=true&pf=110156870,110156873
The physical size will give you a reasonable idea about the rating.
If you have a 125 mW, 4.7 kΩ potentiometer, the current at maximum power is just over 5 mA, so you should never put more than 5 mA though any part of that potentiometer.
To get the LED to turn off at one end rather than dimming slightly, you need to connect 12 V across the potentiometer, and connect the wiper to the LED. With 12 V across a 4.7 kΩ potentiometer, you get around 2.5 mA with no load.
If you have a red LED and a 12 V supply, the LED will drop about 2 V, and so the remaining 10 V will need a current limiting resistance of 4 kΩ to keep the current down to 2.5 mA so that the total current is never more than 5 mA in any part of the potentiometer.
That will give you a quite linear change in brightness, but you will only get 2.5 mA in the LED so it will never be very bright.
If your potentiometer is smaller and the power rating is less than 125 mW, you will need a different circuit.