That will not work well, if it works at all.
First of all, you need pulse width mobulation, or the efficiency will just be rubbish.
That connection, using bipolar transistors active analog area to regulate motor speed will be just as inefficient as the really old "3 way switch + resistor" regulation that some really old cheap brushed electrics had.

Second, the output voltage of the servo PCB board will be 0-5 volts. Thats what its using to drive the servos motor.
The the analog active area of a bipolar transistor is 0,7 volts, +/- 0,1 to 0,2 volts.
The voltages the servo pcb board will output is not compatible with the voltages needed to drive the servo.
This will result in a horrible "on-off" feeling on hte throttle stick.
You will move the throttle stick a bit up with nothing happening. Then suddenly the stick will be very sensitive for a very small travel.

Third, the the drawing lacks a lot of data, its barely a scetch to show a (bad) idea. You need to know a lot more to actually be able to build it.
For example, what transistors to use? What servo pcb board? Which connections on the servo PCB board shall you use?
How to defuse the potmeter of the servo? If the potmeter is allowed to travel, the regulator will be all over the place in operation.

Fourth, a brushed ESC is so cheap that I can hardly see the point of trying to build one like this. The parts list will probably be more expensive than a ready off the shelf unit.
But if you do it as an exercise, then its a fine exercise. But find a different diagram, preferably one with specified parts, and a pulse width modulated one.