Absolutely. Speed vs. Accuracy isn’t quite a fair debate. Most amateur players swing slow and hit it crooked because of poor movement patterns and poor club face control. Think about it: If the club face is wide open during the swing, it’s difficult to swing hard without losing the face completely. Most players slow down their swing to help square up the face.
When we improve a players’ movement patterns this often results in greater range of motion, better leverage, and more force being generated with increased efficiency. All these result in more club head speed. Then, if we improve the face control via grip, wrist alignments, or arm structure, the player can swing harder without the fear of losing the golf ball sideways. Translation: Better accuracy. So yes, it is quite possible for the average player to pick up distance AND accuracy.
At the Tour level this debate is different. Those players already have great club face control and already swing fast. Seeking a 1% improvement at that level is much more difficult, especially when accuracy is so important. Chasing distance at that level is a different ball game and may have unintended consequences. Tour players need to carefully weigh the costs and benefits. But the key is amateur golfers shouldn’t be influenced by tour talk; find a knowledgeable instructor who can help, and see the benefits of improved distance and direction.