I didn't mean using the acronym adjectivally, that would be ridiculous as your examples show ;) When expanding the examples and using the acronym as a noun you can indeed use both forms:

Taxol gains quick approval of FDA.

Taxol gains quick approval of the FDA.

Or others: FDA has approved... vs. The FDA has approved...

To most lay persons, omitting "the" will look a bit weird.

Now the interesting part is that NASA has become a proper noun (probably because it is an acronym that can be pronounced). No one will say "I work at the NASA". With FDA you will see people use both forms, even though the final A in both NASA and FDA stands for Administration. I'm not sure about other government organizations. I don't think anyone says "I work at CIA" or FBI for that matter.