I think he ages, just at a much, much slower rate than human analogs would.
People have already commented that Smith looks much older now than he did just two years ago, and that it's an intentional move to signify how much older and wearier he has grown since his run's began.
But The Master advanced Tennant 100 years, and he looked awful. Matt Smith roamed around for twice that, and looks SLIGHTLY older. Hardly noticeable.