I save half an hour of processing time by skinning instead of plucking. Skinning takes me 1.5 hrs and plucking takes me 2 hrs from live bird to finished carcass. Setup time for the water bath is also reduced.
Sometimes I part out the bird, sometimes I leave it as a whole carcass after skinning (for those I need to pressure cook). For the whole carcass, I put it in an icebath for 2-3 days (simulates the fridge), or I can bag the carcass and the parted bird (separately) and put them in the fridge, laid out individually (not stacked up) to cool as fast as possible.
You can also freeze the carcass directly after skinning or parting, but you will still need the meat to sit in the fridge for 3+ days to get past rigor mortis after you thaw it and before you cook it. When the joints move easily, you know rigor mortis is over and it's ready to be cooked. I've had birds take a day or two, and some take a week or more to get thru rigor mortis. Don't really know why, but moving the joint easily is always accurate for when things are ready to cook.