Alexander Technique won't make you fit, but perhaps surprisingly it often does have a small positive effect in all the three main areas people usually aim to improve when they start a fitness regime:
Muscle strength: Posture often changes as an indirect consequence of learning the technique. This then improves the tone in postural muscles that have become more engaged. It has to be said that the opposite may happen to some other muscles...
Flexibility: As the habitual muscle tension decreases, people may find that their flexibility has improved.
Cardiovascular fitness: This one is really an illusion. The technique typically increases the mobility of the ribcage, and because of this people may be able to run a longer distance without getting the feeling that they are out of breath, and so they think that their cardiovascular fitness has improved.
The main fitness related benefit of the Alexander Technique is in the area of injury prevention. It is tragic that people who want to improve their fitness so often actually end up injuring themselves. Learning to pay more attention to how you do things, better coordination and increased understanding of what your body is really doing will help to safeguard you against injuries.
AT is also used to help with performance technique, for example to correct a faulty movement or posture that is causing sub-optimal results. The most common activities where AT is used to improve technique are running and swimming. Alexander teachers who do this kind of work are typically also experts in that particular physical activity, for example ex-professional athletes, coaches, or trainers.
The beauty of the Alexander Technique is that once you have mastered the basics you can apply it to any activity you want.