The reason humans metabolism engages in chemical reactions that release CO2 is because such reactions release energy. Therefore, reversing these reactions and converting CO2 to carbohydrates and the like requires energy. Plants get this energy from light. I don't of any other source of energy that plants could use to absorb CO2.
Furthermore, the plant to animal ratio on Earth is quite large. Suppose you eat a carrot. Then as you metabolize it, you will release an amount CO2 sufficient for a plant to make a carrot, or carrot-equivalent. So a plant absorbing that CO2 would have to make a carrot-equivalent of plant matter. How many carrot-equivalents do you eat per day? How long does it take a plant to make a carrot-equivalent? If we say "10" for the first question, and "a month" for the second, then you would need 300 plants to absorb your CO2. And if multiple people are in the room at once, then you'll need even more Even if you aren't spending all of your day in the room, for the time that you are in the room, you're going to have to have the full CO2 absorbing capacity, unless your time in the room is short enough that CO2 doesn't build up.
There's also the fact that "stale air" is not just about CO2. There's all sorts of other issues, such as sweat.
Rooms aren't generally air-tight, and basic ventilation is generally enough to deal with CO2. If it's not, it's much easier to build a more advanced once than to fill the room with plants.