Yep, that's where it goes. Last time I changed my air filter I broke the vacuum tube because it was old and brittle. I got some replacement tubing at the auto parts store and re-plumbed it.
There's a little elbow on that big rubber tube that goes from the valve cover to the top of the air cleaner housing. It just pokes into that little elbow. It doesn't seem to me that there would be much of a signal there. Maybe it's monitoring for positive crankcase pressure which would indicate that the PCV system is not functioning.
I doubt that's causing your idle problem, but it's worth hooking it up. Also, I would put the air filter in because the fuel system is probably expecting a certain amount of vacuum in the airbox.
Experience is something you don't get until just after you need it.