The short answer is "YES", surprisingly, it can. Alexander Technique helps you to let go of excess tension that can build up unnoticed in the whole of your muscular suit. The reason we don't notice this tension is that it is always there, it is a long term habit. For example, you may have a habit of clenching your jaw, or pushing your tongue onto the roof of your mouth, or tightening the muscles around your eyes. Take a little bit of time now and let go of some the tension in these areas.
Did you feel it let go? Did you feel the tension before you read this and let it go? Probably not. By raising your awareness of tension holding patterns you can let go of them and decrease the muscular tension throughout the whole of your body. This includes your neck, back, stomach, chest and legs. When this tension releases your whole body expands and decompresses. It lengthens upwards.
This is how you can grow taller, sometimes by inches in minutes!