This is a similar question to dealing with motor contributions that last a shorter time than the fault contribution from the system. Your solution would give the same results as that suggested by Gary B in
http://www.arcflashforum.com/showthread.php?t=37.
Basically it is additive with time because the equations are linear with time. At least this is the case with the IEEE-1584 equations and the Ralph Lee equations. If you are using ArcPro, you might ask Kinectrics to confirm your approach.
You can't find the energy for the the current contributions independently because the equations are not linear with current.