Is there a way to automatically, make a sketch line the max length it can be?

The line is constrained on each end to a different curve. I would like to make the line as large as it can be without actually calculating the distance!

Well, not directly, but you can do a little geometric setup to acheive that.

Figuring that the line is going to be longest where one spline is a maximum and another is a minimum, you can deduce that the slope at these extrema will be horizontal. So draw a horizontal construction line from your spline at a location near its maximum and add a tangency relation between the construction line and the spline. Do the same thing for the spline below it and draw your line connecting the two construction lines. Something like this:

Well, not directly, but you can do a little geometric setup to acheive that.

Figuring that the line is going to be longest where one spline is a maximum and another is a minimum, you can deduce that the slope at these extrema will be horizontal. So draw a horizontal construction line from your spline at a location near its maximum and add a tangency relation between the construction line and the spline. Do the same thing for the spline below it and draw your line connecting the two construction lines. Something like this: