Yes. Yes absolutely!
And a centrifugal governor in no way resembles the internal state of a steam engine.
And it doesn't matter.
Observing inputs and outputs is enough to control weight.
e.g., I've recently discovered that my unexplained weight gain (which over the last year looked like 4-5 step functions, rather than anything continuous) is a result of Niacin (Vitamin B3) deficiency.
That's something I discovered (accidentally) by observing inputs and outputs, the input being B3 supplementation (taken for a completely different matter), which quickly undid all the weight gain (and a lot of other symptoms).
10 or so Doctors (specialists and generalists) and nutritionists have seen me over the last 15 years for my weird weight. Not one ever suggested B3 might be the problem, or ever had a test that would indicate I'm B3 deficient -- although, I have reason to believe I've been deficient for at least 20, and possibly 30 years.
So, yes - observing input and output is definitely enough to control weight. But as this anecdote shows, it's not necessarily the caloric balance, which is what you stated in the first place.
What we're arguing about is the boundaries of causality. Take mental illness. Some people get fat because they have a mental illness. What's the cause of their obesity? Caloric balance or the mental illness?
Depending on the boundaries you draw, one or the other, or both.
Same caloric input, same exercise (that is, main control signal for caloric output the same). Difference in input is a substance without caloric value. Huge difference in weight.
The only caloric balance here at play is the tautological one ("caloric balance was positive as evidenced by gaining weight. later, caloric balance was negative as evidenced by losing weight"). Other than that, assuming you believe this anecdata (which you may not), the notion of caloric balance is useless.
(And, feel free to disbelieve anything I say, but read on B3 and you'll realize there are numerous reports of reduced weight that starts with B3 supplementation, despite no other change in intake or exercise)
Only in the tautologically meaningless sense, in which you define "calories in" by "what the body laters takes out at some point".
Everyone agrees carbohydrates provide 4kcal per gram, right? Well, cellulose (e.g. paper) is a carbohydrate as well. But eating it does not provide you with energy. Xylitol is a sugar alcohol, which, when first introduced to a diet, makes zero (0) kcal per gram available to the body, but apparently settles at 2.7 kcal after a couple of weeks of consumption, in which the body ramps up the enzymes that can actually digest it.
Furthermore, the amount of fat your body uses for e.g. skin lubrication, can vary by a few hundreds of percents (depending on factors not perfectly understood, as far as I can tell), so the "energy out" balance also includes "energy in the form of fat used for mechanical purposes".
The "calories in - calories out" balance is a very crude approximation, that works for most of the people most of the time - but there's a very significant chunk of the population (under their present living conditions) for which it is completely useless.