Not as far as quality goes, but yeah, it matters to me. An Italian brand bike made in Taiwan isn't an Italian bike, it's an Italian brand bike.
Like when I was looking for a new frame a few years ago, I was enthralled with the atmosphere of Italy after seeing the Giro broadcast on OLN, I wanted an Italian bike, made by an Italian master. But it went further for me. I knew that Masi no longer made Masis, and seriously doubt that Ernesto Colnago or Irio Tommasini still brazed up the bikes that bore their names. Doesn't mean that Colnagos or Tommasinis are any less terrific bikes.
But I wanted a bike made in Italy, by the guy whose name was on the frame, not by a bunch of hourly paid workers in a factory. And I re-discovered Mondonico in my search. Built by Antonio and Mauro Mondonico themselves, in their own little workshop out behind their house. An Italian bike.