I recently asked the same question for Cycles, but now I'm curious about the pros/cons of using Blender Render instead - can a curve's tangent be used to define the color of its beveled/tessellated output mesh?
While not used very often, Blender Internal has support for node based materials. Almost the same node setup can be re-created in BI by changing the emission for a material node and the one missing being the Tangent node. While not the same result, the Global output of the Geometry node gives a similar effect. If you wanted a matching result between the two you could use Object output from the Texture Coordinates in cycles to get the same result or with some extra math nodes you may be able to get the BI nodes to give the same result as the cycles tangent node.