You would tinks so...but it really depends, I was running the stock turbo with an Apexi filter..the induction noise was loud as, I changed to a larger turbo with stainless induction piping still using the same filter and the noise is now close to a stock airboxed skyline (Maybe 10% louder) So I imagine it depends on the design of the turbo! A few of my mates have experienced this also so it leads me to beleive if you want loud induction the stock turbo is best!
I agree...the induction noise of my car before the upgrades was insanely loud and actually a little embaressing as with the stock turbo even giving it a little bit of throttle around town to make a lane change or what ever would cause it to make that stupid sound ><