Can entity start following trajectory from any point on the trajectory?

Can we set entity on the trajectory (or close to it) and expect that entity will travel remaining trajectory path if FollowTrajectoryAction gets started?

For example on the image bellow we have entity (black rectangle) that arrived on point 1 without any active actions. Then a point 1 entity's condition becomes true and it is time to start FollowTrajectoryAction. Now the question is should this action make entity follow remaining part of the trajectory or should it fail to start because current point isn't the starting point? Note that we don't know where is the start of trajectory #172 (closed) .