Last fall, I dug up a couple of hot pepper plants which had survived the first light frost in the garden. I brought them inside, hoping to ripen the last few peppers which weren't quite ready for harvest. To my surprise, those two plants have continued to blossom and produce peppers all winter....just sitting in a window with partial sun. These are tiny peppers, but so hot that one goes a long way. I doubt that this would have been practical with larger veggies like tomatoes without grow lights.
Growing veggies won't produce any more of a moldy smell than any other house plants. In fact, arguably, all the greenery will help freshen the air. If you try to do it large scale, your room will probably start to smell like a greenhouse.....earthy. Many people like that smell.