TL;DR - Yes.

The Holocaust (although the term itself was not yet as strongly asociated with the events in Nazi germany in particular as it is today) was mentioned many times in European and US press from late 1942 and onwards. The first instances I'm aware of in non-occupied areas are the articles and broadcasts that followed the Joint Declaration by Members of the United Nations on December 17th, 1942. This declaration was read in the House of Commons in the UK and reported by the BBC, it also made the front page of the NYT under the headline "11 Allies condemn Nazi war on Jews".

Now, this isn't to say it hadn't been mentioned before, just that I'm not aware of it. I believe some Jewish publications in the US might have written about the situation in France based on testimony from escaping Jews after the fall of France. In either case, the full scale of the atrocities in Nazi Germany did not become known in one go, it was more a case of the true scale of the horrors gradually becoming known.

If we include non-free press there were numerous publications made in occupied Poland by underground publications like Polska żyje (Poland lives) and Biuletyn Informacyjny (The information bulletin) from 1940 and onwards.