where will all the displaced heat go? have you talked with a contractor about this or did you purchase your own equipment? I wouldn,t imagine a contractor recommending a space like that for your unit. If he did time for a new one.

The A/C would be plumbed through an outside wall in the same way it would be mounted in a window. I guess my question has to do with whether ducting off the front of an A/C makes sense if the duct is running a short distance, about 4ft.

are you talking about a window unit?

Yes. A window unit I have not purchased yet. I installed an exterior door where one did not exist...which is more complicated then putting a sleeve through an exterior wall. Anyway, as I've thought about this, I've concluded that I've wasted a few people's time on the subject and apologize for that. Perhaps the inquiry will help others. Thanks very much.

The fan in a window unit is not designed to work through ANY duct.

They are designed for the intake filter and coil loss in the unit, and enough to then blow air a short distance into the room through the louvers on the unit.

When posting declare the type of equipment in the OP so we are not guessing as to what in the world you're talking about.

You could make something like this work with some flex duct and in-line blowers. The question is would it be worth it?