Your explanation doesn't seem plausible to me. If your stomach and small intestine is working properly, the bulk of the bacteria shouldn't see much sugar. Afaik the mechanisms how the intestines regulate the gut flora are not well understood. At least not to the point where there are any working treatment for the many widespread digestive problems. There is some slow progress around fecal transplant research.
There's a bunch of "in mice" research on it, but with actual humans it's really hard because we don't yet have the tools to measure the baseline composition of gut bacteria before and after the experiment.
It's all mostly just anecdotal and empirical.
Same with the fecal transplant stuff, which (AFAIK) basically replaces one persons gut biome with a different one. Which causes cravings to change completely for the recipient, in some cases resulting in weight loss.
Which, to me, kinda tells that it's not a willpower or brain thing, it's just the gut biome controlling what you "want" to eat.
