So when a radiator overheats I know it sends excess coolant into the overflow bottle, but if the radiator was low, would it also suck the necessary amount from the bottle? I understood it to be an overflow bottle only.
Easy, look at your overflow bottle when your engine is stone cold, it will be lower than when your engine is hot.
When the coolant is hot, it expands and the extra fills the bottle. Likewise, when the engine is cold it pulls coolant from the bottle back into the engine.