I'm planning on growing a closet also, just for ease, but I don't live with my parents anymore, I moved out, but my mom is still a nosy so and so, and will undoubtedly pop round, so I too am gonna use precautions.
Your precautions tho are valid, but not practical.
How tall is this trunk? 4 foot high?
Because thats how tall your plants are probably going to grow, then they are going to be maybe 1 foot wide, so your going to need a trunk 4x1 JUST for the plant.
Then your going to need a light, an ordinary bulb wont do it and even using a small fluro, your going to need more than one in there.
Lets face it, you locking your closet, with 2 fans in there, isn't going to be suspicious?
So you take the fan's out for safety reasons.....

Then there's no wind, the stalks are going to be as thin as a toothpick, and there won't be any circulation, so your plants will die due to lack of Co2.
Also, plants need "relatively" regular patterns, for example, you can't have 12 hours dark/light one day, then 18/6 the other day, unless you don't want your plants to know what day of the week it is, so they will never veg and subsequently never flower.

I know your saying your going to move them from the box, but they won't have light unless you put lights in, and then if the box is literally TINY, the heat would be too much.

Not trying to ruin your dreams, but it actually take quite a bit of planning if you want to grow them properly.

See I had the plans, and not the finances, so my plants are all spindly, fortunately, thanks to saws advise *plug THANKS SAW!* my plants are probably gonna pull through till next week when I get me a HPS.

Not being negative, but with what your saying, those are the problems I see with your plans.
I'd be happy to discuss what I know with my *so far* limited knowledge about closet growing.

EDIT:
After reading your post for a THIRD time, lol, (half asleep)
If your going to lock your room, then dont bother with the grow box, because it's just going to complicate things.
If you can lock your room virtually all the time, get some ozone bulbs which your getting already (read another of your posts) and just grow in the closet, not in the small box. It simplifies things, provides greater air flow naturally, allows the heat to dispurse from the lights, if there is any, and wouldn't limit there growth.