If you aren't careful, your conical could suffer from the dreaded "suck back" of Star San if you cold crash with a blow off tube attached. This is due to a vacuum effect that is created when the temperature of the beer is lowered and pressure drops inside the fermenter. Star San in finished beer is no good!
Simply remedy this issue by attaching the gas manifold to the blow off port before you cold crash! Apply a small pressure (~5psi) and then cold crash your beer. The applied pressure should offset the vacuum created and seal your kettle from up taking Star San, oxygen etc.