Yes, in that case you will need to track the shape. And you’re pretty much stuck with having to adjust it manually when the line returns to the left edge.
Second, more complicated but more automated option:
For a faster automated tracking, you might want to try is making a comp that is just a bit taller than the height of the green line, then isolating green only with channel combiner or keylight or some such thing. Then fattening the line (with minimax) and rendering out at a lower resolution (like quarter resolution). Then you could motion track it with a very wide tracking area, but it should be 16 times faster at quarter resolution. Apply result to a null. Then you will have to copy the tracking results (i.e. the null) to your main comp and scale it up using a new null. Parent the tracking null to the new null, scale the new null to 400% and unparent.
Hard to say if that is going to be any faster, since there are more steps.
Kalleheikki Kannisto
Senior Graphic Designer