It's possible to get an Arduino to drive any number of motor or servos, provided the microcontroller in question has enough PWM channels and enough power is provided to the servos to drive them.
You'll require 8 PWM output channels in total. 4 channels at 490Hz PWM for the motor ESCs and another 4 channels at 50Hz for the servos, (or perhaps a higher frequency in the case of digital servos). Arduino boards capable of driving this number of channels include the AVR based Arduino Mega or any of the ARM based microcontrollers.
How the servos are controlled during flight really depends entirely on your code and the number of transmitter channels you require to control them.
For example, in the case of the tricopter the servo controls the aircraft's yaw motion through the flight controller's motor mixer. The servo itself is driven by a PID control loop that causes it to not only respond to the pilot yaw stick input, but also to react to oppose any unwanted yaw rotation detected by the gyroscope.