No, you cannot use things like FDA as adjectives: there is no such thing as **FDAer regulations* or **FDAest regulations* — nor can anything be **very FDA*, or **more FDA* than another any more than regulations can ever "be" FDA. So it is not acting as an adjective there.
However, even though they cannot be adjectives, it’s perfectly fine to use them as attributive nouns instead: FDA regulations.
In noun phrases like — well, like noun phrases, for example — the noun noun is there acting as an attributive noun, not as an adjective.
Similarly in the first words in each pair of words in chicken soup, paper tiger, house boat, windshield wipers, bus stop, England team, and moon rover.
In contrast, the first word in each of these pairs is actually acting as an actual adjective here: hot soup, Bengal tiger, lost boat, disposable wipers, fast stop, English team, and lunar rover.
For extra fun, compare the job of running in all three of running water, running shoes, and running scared. Only the first of those is normally considered an adjective, while the second is a gerund (and so a noun) and the third is even more verbal no matter how to you read it.
A good but simple test for all this is to try to apply the X=Y formula given a pair like X Y. If it works, then X is acting like an adjective and if not, it isn't. So while we can say that in the case of running water that the water is running, you cannot analogously say that the shoes are running, let alone that scared is running.
In the same way, with hot soup, you can say that the soup is hot, but with chicken soup, you cannot say that the soup is chicken. Using the X=Y test on FDA regulations, we can see that FDA must be acting as a noun not acting as an adjective, since you cannot say that the regulations are FDA. Now, if they were federal regulations instead, then the first word would indeed be acting as an adjective, since you can certainly say that the regulations are federal.