Well, you wouldn't need to use a nurbs cylinder, the cylinder object is only used for an approximation of the cloth animation. Since the final rope is going to be a curve, it is always going to be smooth. So just use a medium res poly cylinder will do. Also your calculation time might be faster too.
If you read the manual, cloth has its own constraints, just animate the parabela like its flying and constaint one side of the cylinder to the parabela and the other end to the ground. After that is run the simulation and tweak the settings for the cloth sim to get what you want.
I suggest you to read through the cloth tutorials and skim the manual. You have the know the system pretty well in order to control your simulation, otherwise, its going to be hard to obtain what you are after. Simulations is a tricky thing, spend the time to go through the manual will save you headaches later on.