Does it really matter how a person stands when he or she plays viola?
Yes. The instrument is to be a vessel for music and emotion. How can they be freely expressed if the body is contorted in some way? So, here are the basic rules:
Feet under knees under hips under shoulders. Stack yourself so that your shoulders are as balanced as they can be on top of your body. Make sure your knees are not locked ("squooshy knees!" I say to my students) and that you feel an even distribution of body weight on both feet-- which should be inner hip-width apart-- and as flat and wide as they can feel. Tilt your pelvis slightly upwards, so the small of your back is flat and stable.
From this position, balance the viola between your jaw and collarbone, with head facing forward and lightly leaning on your chinrest. If your instrument cannot balance, you will need to add height to your shoulder rest or adjust your setup in some other way. Keep your chest open, and bring your arms to the viola. A great analogy is to imagine a coat hanging on a hanger: Imagine moving the sleeves into viola playing position-- the elbows of the sleeves hang down naturally, where gravity tells them to. They do not hold themselves pushed forward, nor do the shoulders shrug up. Your arms should hang just like the lifeless arms of a coat on a hanger. Let your back do the work of holding your arms in place, instead of locking your biceps or trapezius.
See? Feet under knees under hips under shoulders, with relaxed shoulders and arms, heavy elbows, and face forward.
Unfortunately not my best photo, but it does highlight good viola-playing posture. This is from my first Doctoral recital at the University of North Texas.