I blieve that a 600W will give off 5000BTU's.
Thats a lot to cool.
Your temps in the closet will run around 90+F with minimal ventilation.
You will HAVE to spend more than $100 on ventilation.

I worked with 2 400W and spent $400 on ventilation and fans plus $100 for a carbon sock. My temps are still 82F at best. (4h x 4d x 8w)

Like they said, DO NOT skip on ventilation.