First of all, welcome to fitness stackexchange.From your graph and explanation, it seems like your lifestyle and interests/motivation only permits you to do short training for specific period, and then go back to ground zero. Yes, initially, it may seem like it's all the same . You build up fitness up to a certain level after a certain period of time. This may be more or less same for you, but how it may apply to others, we can only tell after considering a few factors.
- At what physical state the beginner is(Weight, genes, health history, fitness level, age, diet, rest).
- How much they spiral down after they stop.
- From what level they start the next phase of training after the hiatus.
Lets explain them one by one.
Some people have quite a good level of fitness even though they don't do any training. May be because of genes or what they do which may involve working in farms that involve strenuous physical work. So, if someone like that starts, their and someone who's regularly unfit and can't even move without help, their results won't be the same. Age, diet and rest also make some big difference in results you'd obtain. Someone who's 60, and someone who's 18, their result won't be the same over a period of time. Likewise people of same age group, where one rests well and eats clean would have better result than, another who lives on pizza and ice-cream and barely sleeps. Talking about diseases and ailments, someone with chronic illness and breathing disorder like asthma, won't be have the same results for the same goal, compared to someone who is medically fit without ailments.
When people stop, where do they end up? Do they still maintain their shape, or end up being 400+ lbs. Depending on that, the results of the next round may vary. Also, the age factor. We all know with age muscle mass degenerate and ligaments and joints become weak.
This one is closely related to point 1 and 2, and also includes any injury, how you maintain yourself in the period, how strong your muscles are, and what motivates them for the next.
So, it may work for you, but it may not work for everyone for all the reasons I mentioned above. Regarding your case, seems like after every training session you are stronger and ready for the next one after the break, which helps you boost up the training in the next session, as you are no longer a beginner, but someone who's back from break and his body is already used to what he did earlier. So, any progressive loading, or intensity may be yielding better results in consecutive sessions. Honestly, I'm not aware of any research, that supports your theory, but if that's your observation and you made effort to note it down, and it works for you that way, then go for it. Also, keep tracking it to see if it's consistent and progressive over longer period, or some random ups and downs. Good work I should say.