Suppose, through some sugical error, the nerves that sense smell were to cross with those that sense sound. Could this person then “hear” a smell? Going further, suppose the region of the brain that deects sight were wired into the auditory nerves-could the subject “see” a sound?
I wonder how the brain would report such sensations? 
I remeber that short story, but his sensory nerves were accidentally wired backwards, so he experienced darkness as bright and heat as cold.
He woke up after the corrective operation saying “What smells purple?”
You don’t need surgery for this; many run-of-the-mill psychedelics induce this effect pharmacologically (and, thankfully, temporarliy). If you are in one of the few jurisdictions where such things are legal, you can try them yourself and see (and hear, and feel, and smell…). It’s not unusual for people who have taken LSD or psychedelic mushrooms to report “hearing” colours and “seeing” music.
If nerves were as simple as wires and the brain was a simple as a computer then maybe.
As a practical matter, the information flowing through a set of nerves is pretty idiosyncratic. In a sense, each nerve’s content is encrypted and only the corresponding brain region has teh key. An auditory nerve connected to an olfactory brain center would be spewing gibberish into the brain, not smelly noises or noisy smells.
Because the whole system is a learning & adapting one, you might be able to learn to associate certain new smell sensations with what other people told you were really sounds. Synesthesia seems to be a natural & in-born example of just that.
The “bandwidth” for our various senses also differes a bunch. I don’t know details, but I’d bet the visual center processes 10-100x the data that the auditory does, which in turn processes 10-100x the data the olfactory does. So wiring your ears to the smell center would involve putting waay too much data in and the resulting sound-as-smell perceptions would never be anything but a crude shadow of the auditory acuity you used to have.