I don't think that is possible. There is another way to get what you want and that is to use Turbulent Displace + AE's 2D Tracker - it took me less than 5 minutes to complete the task. Here's how -
1) remove Wiggle Paths
2) make the small red ball much smaller (you will use this as the target for the 2D track.
3) manually animate the red ball along the path
4) create an Adjustment Layer at the top of the Timeline
5) apply Turbulent Displace - keyframe Evolution or whichever other parameter that suits your needs.
6) RAM preview to ensure that you're happy with the speed etc
7) nest this comp
8) open up the tracker panel
9) hit the Track Motion button
10) hit the Options button and enable Adapt Feature on Every Frame (this forces the tracker to search for the target even as the target's size/shape changes)
11) track and then apply the results to a null
12 go back to the precomp and hide the visibility of the ball
13) copy the ball layer to the tracking comp
14) line up the ball on the first frame such that it's at the start of the path.
15) parent the ball to the Null
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