i need to correct myself. if you work out without eating protein you will still gain mass in the muscle that you trained, but the protein will be pulled from your other muscles and / or your organs. i assume this is not what anybody wants.
the protein doesn't "float around" your body - rather your entire body is made of protein, which constantly "turns over" ( is both broken down and synthesized back ). so you won't suddenly run out of protein and die if you don't eat protein but the total amount of protein in your body will start going down after about 6 hours of not eating protein and will go down faster the more you train.
bodybuilders refer to something called "lean body mass" which is your total body mass minus your fat mass. the goal is to maximize lean body mass. skipping protein for more than 6 hours will always result in lean body mass going down, even if the ONE muscle you trained might be getting bigger.
for 90% of people the weight loss benefits will outweigh the muscle loss downsides - we're on the same page regarding that, the question is - what is the proper timing ?
IMO your proposed timing is a knee jerk reaction of panicking when you see weight go up on a scale and isn't based in science. that said it might work for you BECAUSE it makes sense to you ( even though it's wrong ) and you're able to do it because you believe in it.
in the end diet effectiveness is 90% adherence and 10% what diet it actually is and whether it is scientific or not.
but if you want the most OPTIMUM way to do it, MY suggestion would be to fast whenever you know you will be unable to work out or obtain clean food ( for example when traveling ) and vice versa - try to overlap high protein consumption with heavy training, with protein consumption starting anywhere from about 2 hours before training to 1 hour after training, and continuing for 2 or 3 days after training.
work out is essentially stimulus for protein synthesis ( when amino acids from food breakdown are synthesized back into muscle fibers ) - nothing more. protein is fuel injection and workout is the spark plug. if you want your engine to run at maximum efficiency you time injection and ignition relative to each other, and you also time protein consumption and training relative to each other.
the bro science of 1 hour "anabolic window" is simply a low IQ way of understanding what i am trying to explain here, and a very crude approximation / rule of thumb.
there is a guy ( Dr. Jacob Wilson ) who calls himself "The Muscle PHD" who knows more about this than me ( and runs an entire institute which he founded just to study this ) ... he creates a lot of free content, but unless you're a pro athlete you probably don't need that level of knowledge ...