I decided to give this a try, and it was a lot harder than I expected...
particularly because I figured it should work with multiple lines, and with multi-touch.
(even if you only have one line, you have to make sure additional touches don't break the action)
you can have as many nodes making up a line as you want. all the nodes that are part of a line need the same Group name (and the Control sprite that slides along the line needs the same Group name). The nodes are connected in order of their instance number.
I gave the nodes DragAndDrop behavior so you can change the line for testing purposes.
if the line bends too much, the Control can get stuck (if you change the direction of the touch just before the Control gets to its target node). I added a bit of an error factor in there which helped a lot. It generally seems to work better with touch than it does with the mouse - it is easier to follow the line with your finger on it, than trace it with a mouse...
with enough nodes, you could make some nice curves. it you don't want to change the lines at runtime then make the nodes invisible.