I don't think 300 years is that long so yeah it is realistic, languages like arabic, while arabic dialects have developed and changed, formal arabic had been kept the same for much much longer than that because there is an effort to keep it the same, like we learn it in schools and it's the language used for anything formal (speeches, the news, etc) and it is the language used in writing but not in speech.
I'm not sure if you're going for your own language in your story but if it's not english then I suggest looking at languages from other cultures too, because there are a few that didn't change as much as english.