I have a hard time believing it would make you any quicker around a regular track in our cars, since they tend to rotate pretty well as it is and the TVC is on the brakes already to help you rotate the car. On a rally course sure, and maybe auto-x as well. No need for it on the street. Of course, if your goal is just to have fun getting the back end loose, go for it.
I can attest to myself being faster, in an autocross situation, using my left foot to assist with braking.
Disclamer: Left foot braking is a preference, and has a lot of factors that come into play as to whether it works for you or not on certain cars in certain situations.
I use left foot braking for autocross, and it makes me quicker, but I also have friends/competitors who don't left foot brake in similar cars and they are quicker than me.
A lot of it comes down to what you are comfortable with, and what your abilities + the car you're driving and how it is setup to your driving style. I have been in lazy v8 rwd cars where if you tried to left foot brake(LFB from here on out in the post) the tail would try to come around. Also have been in similar cars where if you didn't LFB, youd be fighting understeer and have a big, pushing pig on your hands. Coming from mostly an FWD based backround, most FWD cars as I have driven them, like some LFB inputs. Even on road course applications, I've used the technique to help rotation in slower elements, and also in quicker stuff to help control the nose of the car.
I say this with a big disclaimer, every situation is different, and knowing how to LFB, and also how to RFB, and when to use them to your advantage, and when not to.