If you work as a pe teacher and run around all day doing cardio, can you still put on muscle mass?

Yes. Lots of physical activity, where you burn more calories than you take in, can lead to a catabolic state where it may be difficult to increase muscle mass. To increase muscle mass requires additional work to promote a more anabolic state, with resistance training and increased caloric/protein intake.
Yes. You will need to eat more and do some resistance training, but hopefully you know this as a physical education instructor.