All you can do is try it. Here are a few thinking points. You are creating a small column of air which has inertia. Your fan will need to have a good static pressure spec to get that dead air pocket moving. People that tried similar with a duct to the side of the case found they really needed a fan on both ends of the duct to get any improvement - temps were worse with only one fan located at either end of the duct. I recommend using HSFs with radial fins like the Zalman, Tt Orb, etc. which pretty much makes the dead spot problem moot.
However, if your HS does suffer from the dead spot problem, there are fans designed to reduce the "dead spot" effect like the Arctic Cooling AF3, 3TC, AF8, etc.; Unincom 8025; some of the Silverstones like the ones with 90mm blades on an 80mm mount plate, etc.
.bh.