With some help from Wikipedia
BCAA's (mostly leucine) help stimulate the mTOR complex 1. The activity of this complex is stimulated by insulin, growth factors, serum, phosphatidic acid, amino acids (particularly leucine), and oxidative stress. When this complex is stimulated, downstream protein synthesis occurs. This system is inhibited by AMPK, which is boosted by exercise. So basically, you cannot build muscle and exercise at the same time. I've heard many say BCAA's prevent or reduce catabolism, IMO slightly catabolic is inevitable during a workout and has many beneficial effects (from the AMPK- increased glucose sensitivity, decreased storage of energy in adipose tissue, increased lipolysis and increased cellular apoptosis). I would just take the BCAA's post workout when the body starts its rebuilding process (mTOR). From an evolutionary standpoint it makes sense too, hunt down the meal then eat.