Do I need to use the PWM pins in order to control brushless motors Arduino Uno?
No, you need to use PWM in order to control the ESCs which, in turn, control the motors. If you need more PWMs you might add daugtherboard based on other ICs which might provide additional PWM outputs via I2C or serial interface.

In some non critical conditions (ESCs are critical for a quadcopter) you can simulate PWM by switching a plain digital pin HIGH and LOW very quickly, but that is not as reliable as using hardware PWM.