Is it possible to make a gradient over a defined path?
Could you provide a screenshot to give a better idea of how »twisted« the path is?
For logo creation in general you may want to check out Adobe Illustrator, which is targeted at working with Vector data.
This is not possible in Photoshop, however Illustrator CS6 now has the ability to do this:
You can't do it directly, but you can get the same effect:
With your path set up, add a new layer, and a grdient map layer above that. Link those two layers. On the regular layer, stroke the path with a brush, with the control set to fade. Be sure the "Apply per tip" box is checked. If the gradient doesn't go the full length of the path, undo, change the amount in the 'Fade' box, and try again, until its the way you want.
[EDIT] On rereading your post, I see you are just asking about a black-to-white gradient. In that case, you don't even need the Gradient Map layer.