Alexandra E. answered 04/30/19
Experienced part-time writing tutor
I suppose it's possible, but it's highly unlikely. If you live in a country where the main language isn't English and you learn English only by talking to other English speakers, you would never technically learn to read or write it, but you would still have a foundation for both to work off of, so it likely wouldn't be difficult for you to recognize written English or to read or write the language.
However, if you were to learn English through a school or program or by visiting a country where English is the main language and immersing yourself in it, then I would have to say no. It is almost impossible that in these types of settings you would never learn to read or write the language.
Lastly, while fluency, by definition, doesn't necessarily require you to be able to both speak and write a language, one could argue that if you can't, you aren't really fluent.