*Or anywhere not in New York. I'm asking in terms of the broad travel of the news.
Edit: Assuming the hypothetical worker is male or female is fine; I'm not sure if that would impact the answer.
You would hear about it the following day when the papers came out, it was big news around the world. For example I just pulled up my countries newspaper archive and the very next day on the 27th of March a story is in the paper about the disaster.
http://trove.nla.gov.au/ndp/del/article/26336192?searchTerm=triangle%20shirtwaist&searchLimits=
By 1911 you have entered into the mass communication era, telegrams and the wire services had allowed for the rapid spreading of news.
As for the second part of your question I cannot really speak in hypothetical. Many people continued to show up for work and things would have continued on as normal. However in other cases Trade Unionists and Socialists did use the fire to try and bring about change people like Rose Schneiderman in particular fought heavily for change in the immediate aftermath of the fire.