Confused with the effect number of decimals at the output of transducer
In terms of accuracy would increasing the number of decimals make any
  difference in the accuracy?


The accuracy is specified as 1° up to wind speeds of 35 m/s so, acquire the number with enough resolution to avoid making the accuracy any worse than 1°. In other words you would need one decimal place to be confident.


  And in terms of resolution would increasing the number of decimals
  make any difference in the resolution?


The number of decimal places is the resolution. It doesn't give more accuracy but it does allow you to see small changes of wind speed if that is important to you.