It is definitely possible, but I only had several minutes to play around with it real quick. So I can't account for the range of possibilities and quirks, etc.
But try this:
1: Go into the Octane material you have assigned to the hair object, and go to the Diffuse channel.
2: Add a C4DOctane gradient as a texture in the Diffuse channel.
3: Go into the Gradient config, and then click the Linear button.
4: Click the little triangle next to "Amount", to open that config.
5: If there isn't a Transform and Projection already, click the buttons to make them.
6: In "Projection" config, change "Texture Projection" to "XYZ to UVW"
7: In the "Transform" config, change the type to "3D Transformation"
8: Then start playing with the R.X, R.Y, and R.Z values. You can do this with the Octane previewer open and see the color gradient positions change in real time.
There are some quirks, such as the gradient along the hairs seeming to have a limited distance before they repeat. But later I'm going to dig into whether or not that can be adjusted automatically by choosing different settings somewhere (such as changing the UV settings for the material itself, but a quick experiment didn't seem to do that), or by doing it programmatically.
But the above is what I could come up with when I squeezed in several minutes of playing around with it in-between some other stuff.
