I don't really know a ton about this subject, but my understanding is that fasting increases HGH via a reduction in blood glucose (and to a lesser extent free fatty acids), independent of factors like insulin. A common theory suggests that this is due to glucose's stimulating effect on somatostatin (which is also known as growth hormone-inhibiting hormone). With somatostatin out of the way, HGH is released freely from the pituitary.
So BCAA's would increase insulin, but not glucose (or FFA's) levels, so they probably wouldn't have a significant effect that way. But factors affecting growth hormone secretion are pretty complex, so they might have an effect a different way.
Unfortunately, I haven't been able to find a study examining the effect of a BCAA supplement on HGH levels in a fasted state, so I can't say for sure what the effect they would have. But I'd say keep the BCAA's since they have benefits and I don't know why they would blunt HGH as of now.