The idea of a fouling shot, if I understand it correctly, is not only to deposit a layer of fouling on your barrel but also to raise the temperature up a little which will affect harmonics and impact of the next few shots. Shooting a round to store it fouled doesn't make sense to me- your first shot is still going to be different because of the change of temperature. In other words, I might shoot a fouling shot at a competition because that first round out of a clean, cold barrel is going to impact differently... but it's only useful if I plan on shooting a string immeditaely after that.
I was taught by everyone from competition shooters to marines that you shoot your gun, clean it well, leave a thin film of oil and lubricant, and put it away. This storing fouled seems like nonsense unless you mean you are storing your gun dirty because you haven't had time to clean it.. a lot of times if I shoot late Sunday afternoon I don't get around to cleaning until mid week (though i always spray some CLP down the barrel ).
If you are cleaning your gun and then shooting a round through it to purposely avoid the condition of the first shot being slightly off I think you are overthinking things by a wide margin. Also, the more you shoot the more you are changing the buildup on the rifling so no 2 shots can be exactly equal anyway except for the first shot out of a clean, cold barrel.