Given I have kegs, I have never cold crashed in a carboy...no reason to. Rack from the primary to the sanitized keg, seal with co2, vent, seal with co2, vent, seal with co2 to a pressure where you are sure the seal will hold. Then use the keg as your secondary/conditioning vehicle. Then, do your cold crash as close to 32 degrees as you can. (In reality, the beer won't freeze until about 28-29 degrees, depending on the alcohol level, but I'm afraid to get too close just in case my temperature is off and due to the cycling range of the fridge.) If you want to hurry the process, you can have gas applied at whatever temperature you need to get the correct psi. After a couple/few days, the crap will be at the bottom and you can draw a couple of yeasty, messy pints off.
An alternative to drawing off pints is to bend the beverage line slightly so that the very bottom of the liquid won't be drawn out. Your gunk will be there. Another alternative is to cut off 1/4-1/2" of the beverage line. Both of these methods (which I've used only on one keg) have the advantage that you won't clog up your beverage line or poppet. (Which I've done on one batch, and that was when I had a bunch of hop gunk.)
After a couple/few days, raise the temperature to proper serving temp and allow your carbonation to continue until its ready.
This, plus using Irish Moss, has really, really cleared up my batches as compared to when I didn't do this.