My sense is that in any amount that you are likely to be taking them, they should not interfere. The question is whether the BCAAs will result in any significant insulin response. I don't know about that, but I have seen studies that suggest that BCAA levels in the plasma increase during starvation. I expect this is because BCAAs are readily oxidized during exercise and during starvation or fasting, they are released to provide a systemic energy substrate. I'm speculating there, but it seems reasonable. So, BCAA supplementation is mimicking your metabolic response, which I would expect to maintain the fasting hormonal context.