I heard that if you feed cats processed cat food for a period of time, their palate/stomach will be unable to eat natural food again (meat, rat, etc). Is that correct?
It's not really true - at the physiological level, I certainly cannot see how prolonged consumption of processed food could disable a cat from being able to digest natural food. However, I could see the trace element of truth in this statement's essence, which might explain it's plausible origin.
Cats, compared to dogs, are known to be a bit of picky eaters. Unlike dogs, cats could literally starve themselves to death in case of the available food not suiting their fancy - that's how picky they could be*. At the same time, please take into account that it's in the cat food manufacturers' best interest to make their products as tasty as possible, and they certainly have all the necessary means to do the research and come up with the optimal formula.
As a result, transitioning from processed cat food to natural food could in a way resemble - apologies for not coming up with a better analogy - transitioning a child's diet from prolonged dining in fancy restaurants and eating pizzas with a whole variety of alluring flavors, to unseasoned and blandly-tasting homemade food. The child would surely be resistant and need some time to transition - which, as other answers already mentioned, is the case in all diet changes - but it doesn't mean that the child's physiology and metabolism had been changed in a way that disabled them from digesting natural food. Like the child in this hypothetical scenario, a cat could just get psychologically used to a certain kind of tasty food, forming a deeply-rooted habit.
My analogy to human diet is obviously not the best and it's not directly one-to-one - yes, cat food manufacturers don't enhance flavor by using spices known in human cuisine, like black pepper, chili, onion, garlic, etc. Not only cats experience taste differently from humans, but also some of the human cuisine spices are extremely toxic to cats.
But my point still stands; as Trond Hansen noted in the comment, cat food manufacturers are using flavor enhancers, known as palatants, which could be seen as analogs of spices used in our human cuisine. Also, manufacturers do in fact research for the optimal texture, humidity, salinity, tenderness, etc. of the food to suit cats' fancy as much as they can. A cat used to this kind of food could just have been in some sense addicted to a great taste (addicted in the sense of psychological habit, not physiological dependency, though) - together with the before-mentioned cats' pickiness, attempts of such diet transition could give the convincing, albeit completely false impression of their inability to eat natural food ever again.
References to the statement marked with asterisk:
No, that is categorically false.
Now, it does take a cat some time (on the order of a week or two) to adjust to a new diet. But that's true of any new diet, whether you're moving from natural to processed, processed to natural, or between two different types of processed food. It's possible that whoever started that rumor just misunderstood the fact that cats need time to adapt.
It's also possible that a cat raised in captivity and kept indoors all the time might not know how to hunt their own food. In this case, it's less a matter of being unable to eat "natural" food, and more about being unable to get it in the first place.
As Fraxinus has said this, in practice doesn't make a whole lot of sense.
A lot of cats are known for begging for almost any food, just like dogs, and as the owner of 3 cats that are fed procesed cat food I can personally attest that they will eat anything. 1 of them goes and hunts birds and mice all the time and the other 2 will eat chicken or bacon or pretty much anything I give them.