It does also help with insulin sensitivity via glucagon, but I still don't think it'd be ideal during IF, even though I've heard of that protocol. I remember someone asking Robb Wolf about this aspect of LeanGains at some point. He thought it was legit.

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.

There are three BCAAs: leucine, isoleucine and valine.

Per this source (emphasis is mine), http://pathman.smpdb.ca/pathways/SMP00032/pathway:

In muscle, the final products of leucine, isoleucine, and valine catabolism can be fully oxidized via the citric acid cycle; in liver they can be directed toward the synthesis of ketone bodies (acetoacetate and acetyl-CoA) and glucose (succinyl-CoA).

Because isoleucine catabolism terminates with production of acetylCoA and propionylCoA it is both glucogenic and ketogenic.

Because leucine gives rise to acetylCoA and acetoacetylCoA, it is classified as strictly ketogenic.

From that information, I'm going to take an educated guess that perhaps if you supplement with pure leucine, you shouldn't invoke an insulin response as you'll remain fueling your ATP production with ketones.

This answer's coming a little late, but I think it's worth noting BCAA's are usually only recommended if you plan on doing heavy lifting in a fasted state. The research that supports IF, which is not eating for brief periods of time, also supports not needing supplements during that time to preserve muscle. I IF every day and I don't take BCAA's unless I'm working out, in which case I'll take down about 10g an hour until I break my fast. Usually that only requires one serving though.