Some study was performed by an undergraduate thesis and the conclusion was:
The purpose of this study was to determine if supplementation of BCAAs in combination with glucose would reduce exercise-induced delayed onset muscle soreness (DOMS). (...) there was a statistically significant difference between BCAA and placebo for females at the 24-hour rating (p=0.0182).
Another study concluded that BCAA without tyrosine reduced mania symptoms, but I don't think that's the claim you're looking for (specially because it's a specific formulation for a BCAA, not the one sold to improve recovery after exercises).
And for specific sport-related analysis, there was an study about the use of BCAA to increase endurance of running:
Em conclusão, a suplementação de BCAA não afetou o desempenho de endurance em um teste de corrida até a exaustão (original)
The conclusion is that the BCAA supplementation didn't affect the durance performance in a test of running until exhaustion. (translation)