The second option uses much more runway than the first before the application of take off power BUT the aircraft already has forward momentum. Does this forward momentum equate to reducing the runway required over the 90degree line up technique.
The general answer is no. It is more efficient to line the aircraft up properly. Hence, the performance data is based on a proper line up.
However, in your question there are a 1000 variables. SOMETIMES is might be more efficient to make a rolling takeoff. Depending on the turn required etc. Even tough you have momentum, it will be fairly small if lining up through a 90 deg perpendicular taxiway. If lining up at a rapid exit intersection, obviously you can carry more speed onto the runway.
If your performance accounts for sloppy lineup, or the runway length is not a factor, of course you can safely do a rolling takeoff. If the runway length is performance critical, do a proper lineup coming to a complete stop before applying takeoff thrust.
Also, perpendicular taxiways never have rapid-exit taxiway lines. In any case, there is no point in following ANY taxiway exit lines, as they are just that = EXIT lines. Turn the aircraft as sharp as feasible and appropriate for the current taxi speed, disregarding the exit lines.