Push Button to Drive Power to Servo
There is a chance that this arrangement could damage the servo and possibly the Arduino.  The problem is that, depending on the internals of the servo, it could try and draw power for the servo through the data pin when the button is not pressed.  This would both over-stress the internals of the servo and the internals of the Arduino's GPIO pin.

What you could do to mitigate that is to connect the servo's switched power to another GPIO pin of the Arduino, which is set as INPUT.  That will then tell the Arduino when the button is pressed and when it's not pressed. Then you use that information to attach and detach the servo in your code so it is only being actively driven when the button is pressed.