Yep. You need to install everything that goes in the wall and out the wall or roof, leaving you with a hole placed exactly where you are going to hang your unit and electricity to that place.

Somehow, on our house everybody forgot to actually put in the vent through the roof until it was finished. The day I came out and admired it I finally clued in and said, "Where's the stove vent?" Fortunately, the stove's on an ouside wall, so instead of a major tearout (I didn't have to find out if there was now a loadbearing beam in the way) we just directed it straight out. The fig tree and rose outside, to my surprise, don't seem to mind, although they look pretty funny when it's on.

Forgot to mention for the rest of your question, our trim carpenters built a frame on the blank wall out of 2x4s, framing a now-fake shallow chimney to the ceiling and a deeper and wider section below that (I wanted to create a shelf for display) of the dimensions needed to enclose the unit, which was then mounted on the inside of this very sturdy framework.

Note that this all occurred after the wall was drywalled and the windows trimmed. The cabinets and stove could already have been installed but weren't.

My design wasn't even complete at install, as it turned out. When they were putting it together I decided the shelf needed to be higher than I'd drawn it to look right with the lines of the double-hung windows on each side, so I sat there and had them add wood to raise the shelf level three or four times (I'm afraid it really was four) until it was juuust right.

In any case, I'd suggest not buying an expensive hood of inflexible size from a catalog of designs (in case you're considering that) since one could be built on site exactly as needed and then finished as desired. I developed my design using a couple of lovely hoods on the Finished Kitchens Blog as inspiration.

Thanks, Rosie. Our contract specifies adding exterior venting, so the hard part is already planned for. It's just deciding about the aesthetics that's hard...