In my opinion, absolutely not. Yes, it is true that BCAAs do not contain any calories, but they can also ruin your chance of getting any of the benefits you would have gotten had you only opted for drinking water. Additionally, understanding a few simple things about BCAAs will help you realize why doing this is a complete waste of money.
They are amino acids that bypass the liver and get directly into your blood stream. The theory is that they work to activate the mechanistic target of rapomycin or mTOR. This is the pathway through which muscle protein synthesis occurs. Many scientists believe that of the three BCAAs, leucine, isoleucine, and valine, leucine is the most responsible for this.
Primarily because of what I just mentioned. Activating the mTOR pathway would deactivate fat mobilization and shut down the fat burning process, which is one of the reasons why most people fast in the first place.
Additionally, it would also shut down one of the other primary benefits of the fast, which is cellular apoptosis - the process by which your mitochondria clear out diseased cells to make your healthy cells healthier.
Taking BCAAs in a fasted state makes no sense because the primary reason people take BCAAS is to enhance recovery and build muscle mass. In order to build muscle mass, all 9 essential amino acids (EAAs) would need to be present. These are the amino acids that your body does not produce on its own and needs to acquire through nutrition:
BCAAs contain 3 of these, but not all 9. As such, taking them in a fasted state when other amino acids are not present in great enough amounts for them to help with muscle synthesis would be a complete waste.
You don't need to worry about catabolism during your fasting window because of ketosis. Intermittent fasting works by leveraging your body's ability to mobilize fat for fuel, creating a state of ketosis. In this case, as your body is using fatty acids, or ketones, for fuel, it would not need to break down muscle for energy. This would again negate any reason for taking BCAAs.
BCAAs would be more helpful if you were on a lower calorie, but high carb diet without fasting, to protect your muscle mass, but they are not necessary with a keto diet or an IF protocol (at least during the fasting window).
If you really want to take BCAAs then opt for taking them in your eating window where they will have other amino acids from food present to complement them. A better option would actually be EAAs in supplement form during your eating window if you are really trying to use amino acids to build and protect muscle. Additionally, you can simply rely on your food intake to provide all the amino acids you need.
But YOU SHOULD NOT take them during a fast.
For more information on how you can build your body through keto dieting or intermittent fasting, check out my course Warrior Soul Keto Camp.