I think BCAA (particularly leucine) can be beneficial (around your workout).
Leucine is an activator of the mTOR (mammalian target of rapamycin) pathway, which regulates protein synthesis and enhances glycogen synthesis in muscle. Having sufficient leucine levels around your workout ensures a strong mTOR signal. Leucine also activates mTOR is
adipose tissue, causing the secretion of Leptin (the hormone that makes you feel satisfied or fed). So when dieting, I think BCAA or some extra leucine can be beneficial as a 5 grams of leucine (20 calories) would send a stronger fed signal than 5 grams (20 calories) of a whole protein. So you can consume less calories can get a stronger anabolic/anti-catabolic signal. Isoleucine and Valine also have some interesting properties.
Since training depletes leucine levels [1], supplement can be beneficial. Gut it all comes down to cost vs. benefits. From my experiences, particularly when in a hypocaloric state, extra BCAA are beneficial.
1.
Sports Med. 1999 Jun;27(6):347-58. Leucine supplementation and intensive training. Mero A.