It would be better to have the bird in a bag.
Though it will most likely be ok, water and moisture are breeding ground for bacteria. I have worked in resturants for 8 years, and know what some water can grow into.
If your cooler gets too warm, that water will start to grow nasty and smelly things. At least if your bird is in a bag, it will not absorb any of it, though it wont take long for the meat to warm and that same process to begin happening there. Still, the meat will retain the temperature longer than the water around it.
Good luck!