The dog is trained with samples and cultures, not people, so that would look like a no for breath.
OTOH, cancer in a person is inside an organ inside the body, a long way to go to smell it directly. But what we breathe out stays around us in an invisible cloud. To me that looks like a stronger yes for breath.
Electronic nose technology is advancing, but mostly by specialization and rapid chemistry, not direct electrical conversion. I wouldn't hold my breath for anything soon.