Yes, there is still a notion for angular momentum in orbits in general relativity, and so pretty much the same proof of the area law works in general relativity, except that you need to consider the area as being a coordinate area (i.e. not a physical area) defined by the r and theta Schwarzschild coordinates, whereas the time is a proper time not a coordinate time.
For circular orbits, Kepler's law relating the square of the period to the cube of the radius also holds in general relativity. This one depends on you using Schwartzschild coordinates for the time though.
