Ditto to what Dale and Roger said.
If my hiking clothing gets wet, I do put it in a zippered plastic bag at the bottom of my sleeping bag. It's not any drier in the morning, but at least it's warm when I put it on! Since I don't have to heat up the clothing when I put it on, my body heat gets some more of the moisture out while I'm packing up inside the tent.
You can dry wet clothing by wearing it inside your sleeping bag, but most of the moisture will get absorbed by the down, considerably reducing its insulating efficiency. It might be OK if it isn't too cold (like well above freezing) and if you're going home the next morning! The same is true of synthetic sleeping bags--the insulation won't absorb quite as much moisture as down, but it will absorb some.