No it won't. The aircraft is unaware of movement of the air mass in which it flies. Think of a boat on water. On a still lake its water speed will be x knots, which will also be its speed past the ground at the shore/ground). Same boat on large river. No matter which way it points - upstream, downstream or across - its water speed will still be x. It's speed past the ground, however, will vary. Pointed upstream (ie into the prevailing wind for an aircraft) the speed past the ground will be slower. Pointed downstream (wind behind you if an aircraft) the ground speed will be faster. Across the flow then ground speed will be a vector sum of the water (air) speed and the current (wind) speed.
What the advice you read is on about is that high winds can be association with *sudden* changes in wind direction. In this case the change in wind speed occurs faster than the inertia characteristics of the aircraft allow it to accelerate or decelerate so there can be an instantaneous speed excursion. Left to its own devices the aircraft would eventually stabilise back at it original airspeed (but with a now different ground speed).