Can abbreviations be used as stand-alone adjectives when the abbreviated term couldn't?

I see by your name that you are probably ESL…

ESL stands for "English as a second language". In the above sentence, it is being used as a stand-alone adjective, but I’m not sure if that makes sense. The term would not work as an adjective if it wasn’t abbreviated, as in:

I see by your name that you are probably English as a second language…

You can be English as a second language, that’s absurd. However, ESL is used like an adjective (or a modifier, I’m not quite sure on the terminology), in cases like ESL writer or ESL speaker. If it modifying the noun, and modifiers are usually adjectives or adverbs. Because of that, it seems that perhaps it would be correct to use this abbreviation as a stand-alone adjective in the example sentence. Or is this ungrammatical?