Not sure it did when the question was first asked but it sure does now.
Check the sample:
Based on my observation of how the Silverlight SDK works (which has snapping), I believe you will have to write your own snapping implementation. I don't think there's anything on the server that will really help you.
You will have to retrieve the geometries associated with the road(s) you want to measure via the FeatureServer. Then on the measure tool, you'll have to enable a mouse listener to search the vertexes of the visible geometries.