AYTINYx4 - execute other code during analog conversion
-Is this while loop just bad coding or are they doing it for noise reduction (because in free running mode, also other code would be
  executed during conversion)?


The while loop is for waiting until the ADC has finished.  Most ADC conversions depend on ADC configurations which are set prior to the start of conversion.  Such as number of bits, speed of conversions, power mode and ADC clock speed.  So it is convenient to wait until the hardware says it is done. 

I don't see a problem if you wanted to execute code prior to checking for completion of the ADC conversion.

ADC noise is a very broad subject.  If you have a specific question, ask.  Otherwise I would suggest implementing your design based on the particular processor's application notes to see if the results are acceptable.


  -If I put the check for ADSC to be cleared in my main loop, what would be the advantaged / disadvantages?


I don't see any problem with that.


  -If this method is for for noise reduction, how much added inaccuracy (maybe a ballpark figure) can I expect - I can live with +-2 or 3LSB?


More often what I see as noise in embedded processor application comes from outside the processor.  For instance, if the processor is activating high current bright LEDs during and ADC conversion.