With my 3800 II that vacuum hose goes to the HVAC controller as Mike mentioned, but it also Tee'* off from the large wire loom that runs it to the HVAC, and it runs around the body of the passenger side of the car, until it gets to the front area, then it goes down near the front bumper, then across the bumper till it gets to the EVAP Vapor Canister, which on my car is located under the air-box and PCM.
When you let it run for a bit while plugged does it throw any DTC'*?
I'd have it scanned for trouble codes if you have not already done so.
I don't have the diagrams for the EVAP routing on hand, or I'd post them, maybe somebody else will be able to provide them.
2006 Pontiac Grand Prix GT with SC
1996 Buick Park Ave NA