Everything that should be said, has already been said. Trying to keep MPS (muscle protein synthesis) elevated all day is a bad idea. Your body needs the dip. Otherwise, you’ll lose receptor sensitivity to the amino acids that promote muscle protein synthesis, which essentially is the signal to tell the body to build muscle.
If you’re gonna do BCAAs, it’s not bad to use them with pre or intraworkout. Also, if you have a meal that is low in protein, adding the BCAAs via a drink is a good way to make sure you get those vital amino acids too. You don’t need BCAAs if your food/nutrition is on point.
But let’s be honest, it’s better to drink BCAAs than a non-diet soda, so if it keeps you from drinking something high in sugar, then go for it. Not all of us are pro bodybuilders. Some of us just live the lifestyle and want to enjoy things outside of bodybuilding. Because of that; don’t let someone tell you that you can’t drink BCAAs when you want. Just know it’s not ideal and probably not wise to make a habit of.