ChartAreas have Cursors, but I'm not sure you can set them to what you need.

A second less elegant option is to add a new series, set it as Line, add a new Legend to the chartArea, add the second threshold series to that legend and disable that legend so that it is not visible (unless of course you don't mind (or want) to have the threshold series visible in a legend). Set the series to have two values, at [x-min, y-threshold] and [x-max, y-threshold], set it's color and bordersize as needed.

Perhaps not the most elegant solution, but it does the job. On the good side, it would allow you to add a threshold line with different y-values along the x-axis.