Will splitting a duct to extend HVAC to an addition cause problems?
Typically Ducts are sized for the space they are conditioning. Splitting a duct will reduce the efficiency of conditioning that space. You will need to know if the HVAC system has enough CFM Flow for the addition to begin with. Ideally it would be best to run a line direct from the main box coming from the HVAC unit. You could also increase the size of the line to the main unit and then branch from the larger line to the addition. 

Will it cause a Problem in the HVAC System, not really, especially if it is not zoned. If you have a Zone system then your bypass damper may need some adjusting as the back pressure of that run is now lower. 

Scott&lt;-