I'm a U.S. native speaker and I've never heard the word "noughties" here. To be honest, I, and everybody else, actually has a problem referring to the decades 2000-2009 inclusive and 2010-2019 inclusive. Of course, for 2010-2019 we can always fall back on "the current decade."
It's a problem for historic decades, too. 1900-1909? Personally I would say "the opening decade of the twentieth century." Or, sorry, "the Edwardian era."