I replaced HCV and found the hose like you said. I left it hung down car runs A okey.
Like you confirmed must be vent hose. Thanks for postings!

vent valve deception
 

That is the transmission vent valve hose like the other guy said. I just discovered it on my 98 Catera and it has thrown me off track just the same. It may have a tie strap holding it to the 4 vac hoses coming from the intake plenum. Good thing I read your question or I would still be looking myself. Of course my factory service manual does not help here much as it has no Vacuum diagrams in it worth looking at.
05 CTS,98 Catera, 92 Eldorado, 90 Allante, 89 Allante, 88 Eldorado, 88 Limo, 88 Cimmarron, 87 Deville

Thank you for starting this thread :)
I changed the valve cover gaskets (2000 Catera) and was getting P0411 engine error code, knew it was for the secondary air injection (AIR) system so knew I must have broke a line or put it together wrong and was getting really frustrated because I checked all the connections and hoses and didn't notice any holes, etc. I did notice a hissing up by the intake manifold and in the middle of where #2 and #3 goes in the bellow diagram; I need a vacuum diagram for a 2000 cadillac catera - JustAnswer but thought is was a hole I thought was supposed to be there because it is on a little device that I don't know what it's called but since I didn't see any extra lines thought it was a little hole on purpose to let something breath but thanks to this thread and the diagram I realized that the hose for the transmission vent I had hooked up to this line that is supposed to go to this hole I thought was supposed to be there but had broken of the plastic connector tube and didn't realize it until now that was supposed to connect to this spot.

Engine light off now and no more codes :) :) thanks to this thread and diagram