Hello,
Ok, now I understand your idea. Yes, to do this we must add a new Affect parameter: "Vertex color" for the Surface distributor.
But you can solve this problem without using the vertex color map. Use any other procedural texture or animated bitmaps, and then you will be able to influence to the parameter "Instanced geometry -> Current time".
Please see my example...
At first I influenced to the path length, then from the length I influenced to the Current time.
Cheers
growingGrass_Example_1.max