If you're doing Crossfit style sessions, then it certainly is "enough" to get in shape. There's more to strength training than typical body-building workouts.

To be fair, Crossfit's a lot more than "strength training."

Say "strength training and conditioning" and that's exactly what it is.

It is very important to be in good cardiovascular shape. Weight lifting puts stress on the heart and the cardiovascular system as whole. That's why doctors advise cardiovascular exercises to the population (such as walking or jogging)--one will eventually be in better shape, as well as improve their cardiovascular system at the same time.

Of course, having a lot more muscle due to weightlifting will also help one burn more calories, but in order to keep up with the body's progression, and challenge the body with more and more weights as it becomes ready, one needs to have a solid cardiovascular system (for safety.) Also, running would be the best type of cardio (for 30 minutes at a time) as it helps build bone mass in legs, knees, and maybe the back, which also will help prevent injury.