Hi
Yes, the path will still by default end up on the position of the last node in the path.
Usually the Seeker handles this, but the easiest for you is probably to run this right before you run the funnel modifier:
path.vectorPath[0] = path.originalStartPoint;
path.vectorPath[path.vectorPath.Count-1] = path.originalEndPoint;
You might want to snap it to the closest point on the last node in the path, but this should be a good start anyway.
Take a look at the StartEndModifier if you want to know more.