100% real.
Even shadow boxing at home and doing movement drills by myself, there is a massive difference in how loose my body is and the technique and flow of the strikes, aswell as the pop. Everything flows better.
It is noticeable even after 2 weeks of not shadow boxing/moving around.. i am noticeably worse, and i am definitely a fast learner/fast adapter, i've heard this alot said about myself, and i still notice a difference between the dude that has trained in the last 2 weeks and the dude that hasn't. So i imagine when you talk about the big game, and being in a real fight where each move counts and could be a KO shot, it is another level.
It is undeniable, especially the higher level you go.
Imagine if you are really good at Counter strike.. I can not play for a year and steamroll lower ranked dudes that literally play everyday, that never goes away, but if you try and play dudes of your previous higher skill level from when you played frequently, that is where the difficulty sets in and you start noticing it is a bunch harder than you remember.