Yes: Feel your upper body centered as your weight shifts to your left side. No: If your upper body slides outside your feet, you will lose power.
Whether it's a hockey player on ice, a girl on roller skates, or Sam Snead hitting golf balls barefoot, stability is the key to making athletic moves. Jack Nicklaus said golf is played "inside the feet"—meaning your torso's weight should be stacked over your feet during the swing.
Don't let your left hip slide forward on the downswing, causing the weight of your upper body to drift to the outsides of your feet (inset, right). If your weight drifts, you lose stability and power.
Think of it this way: If you were swinging on a sheet of ice, you'd have to keep your weight centered over your feet, or you'd slip. That's a good image. Focus on the feeling that your weight is being supported on the insides of your feet.