Can I safely wire this motion-sensor light?

You could, but it cannot be a switch leg. That means that power would have to enter at the switch. If you have a switch leg, you would need a neutral. That means 3 wires plus the ground.

Follow-up

Thanks, gregzoll! I had to do some research on switch legs before I could respond. A few questions:
1) What you're saying is that with the current configuration of wires, I could not do what I suggested without running an additional wire to where the new switch will be?
2) I will not need the existing switch (outside the closet) after I install the motion sensor switch (inside the closet). Does this change anything? If I deactivated the old switch, could the only switch leg would be to the new switch? How would I do that, and again, would that involve pulling more wire through the wall?
Pulling additional wire behind the wall is beyond my ability. It just seems like I should be able to capitalize on the shoddy outside-the-wall hardwiring job that the previous owner did here...