That is possible. I have had fish tanks in the past with fish in them fully cycled with no filter or pump just plants and they did fine for a long time and there wasn't really any smell. Sometimes there was a slight smell in air but it wasn't really that noticeable. Its amazing what plants can do.
The box is almost complete. I've had a lot to do today so I didn't get a hole lot done. I will try get a bit more done this evening.