No. It would telegraph your punch. Don't forcibly shrug your shoulder. People who have a decent boxing IQ will pick up on your shoulder shrug, and understand it meant the punch was coming. You'd want to throw your punch as natural as possible to prevent telegraph, stiffness, and fatigue. Granted your chin is tucked you'll find the shoulder covers the chin naturally upon extension.
You'll find your shoulder shrugged on either arm as a means to prevent a counter when the punch is fully extended, and then you'd want to retract your hand to your face as fast as possible without looping.
Think of the cover like this when punching: 1) Hand 2) Arm 3) Shoulder then 4) Hand again. If your chin is tucked, and you throw the punches properly you don't have to consciously shrug. The shoulder will more or less cover the chin naturally on the extension. The biggest thing to consider is tucking your chin. I've always been taught chin tucked hands up. This will ensure that something (hand, arm, shoulder) will cover it.