Are Total Harmonic Distortion and Noise (THD+N) and THD correlated in practice?
Q1 Are %THD+N and %THD correlated in practice in the case of common
  audio devices (speakers, headphones, amplifiers)?


This really depends. THD is just a contributor to THD+N. If the noise dominates the numbers can be vastly different and if the THD dominates the numbers are basically the same. Passive components (passive speakers or headphones) have no inherent electrical noise so THD tends to dominate unless you hit a point where you trigger mechanical or acoustic noise as well. A good example of non-harmonic noise is port noise on a vented speaker.


  Q2 How important is %THD in the reproduction of the input signal in
  speakers or headphones?


Depends on your definition of important on what you care about, but specifically in speaker design we keep a very close eye on THD since speakers are fairly non-linear.