It'll make plenty of sound. It'll just be very distorted. Think of it this way: The front face of the speaker cone makes the desired soundwave, while the rear face makes the same soundwave, only counter-propagating and out of phase. If the cone were acoustically invisible (but somehow still magically able to push air to create soundwaves) and the soundwaves coming from the rear face of the cone were magically reflected to the front, the two soundwaves would indeed cancel out. That doesn't happen in the real world though, and what you get is an out of phase signal somewhat delayed, causing all sorts of unintended interaction with the front soundwave.
Some people think the enclosure's function is to resonate, similar to the body of a violin or other stringed instrument. This is totally false. Cabinet resonances are undesirable distortion in a speaker intended for sound reproduction. This is why good speakers are heavily dampened. Although it's a little rough, some people like the "knock test". If you're buying speakers, give the side a few soft raps with your knuckles in several different places. If it booms like a hollow box, it's bad. If it sounds like you're knocking on a solid chunk of wood, that's good.
Not disagreeing, but: Bass reflex designs are an exception to some of what you've written. They essentially use the reflected sound wave you've mentioned to increase the output in certain low frequencies, by letting it out of a specially constructed hole in that solid cabinet.
I'm sure that you're using simplified terms to explain this but bass reflex enclosures don't use reflected sound per se. It's a heimholtz resonator(like blowing across the top of a glass bottle) and the air in the port is in phase with the front of the speaker until it's tuning frequency at which point it rolls off more steeply than a sealed enclosure because of phase cancellation.
My dad had these really in-efficient AR-3 speakers growing up in the 80s (needed a lot of power to drive). When moving they were so heavy, turns out not Base Reflex but a defunct speaker technology called "Accoustic suspension"
Some people think the enclosure's function is to resonate, similar to the body of a violin or other stringed instrument. This is totally false. Cabinet resonances are undesirable distortion in a speaker intended for sound reproduction. This is why good speakers are heavily dampened. Although it's a little rough, some people like the "knock test". If you're buying speakers, give the side a few soft raps with your knuckles in several different places. If it booms like a hollow box, it's bad. If it sounds like you're knocking on a solid chunk of wood, that's good.