Ernest Lehman uses the phrase twice in the source novelette. In both instances it's very much in the literal sense; 'Cheap' smells bad, 'expensive' smells good.
When he 'hits it big', the narrator expects to be surrounded by nice-smelling things and nice-smelling people.
I walked into the huge, thickly carpeted show place that Hunsecker called a living room, past the statuettes and golfing trophies that stood on the table in silent tribute to the man’s self-love, and I sank exhausted into the green club chair. The lights were dim. The Capehart in the corner was playing softly, and as I sat there gazing at the portrait of Hunsecker on the wall, my eyes slowly closed, and I allowed the soothing music and the muted sounds of the city and the rich, sweet smell of success that permeated the room to lull my senses. I breathed the smell deeply, memorizing the scent, and then all at once I became aware of other sounds, other perfumes, and I turned, startled, as I heard her saying quietly, “You’re early, Sidney.”
And
The sidewalks were steaming and the air was heavy with exhaust fumes, but still it was good to be outside, away from the fetid odors of old newspapers and dirty walls and Gloria’s cheap toilet water. When I got my new office, it would have thick carpeting and rich, bleached oak furniture, and the air would be scented with the sweet smell of success.
Lehman is constantly making reference to how people smell in his books and novels. Generally, for example, you can tell a class of woman by her scent. Whores wear perfume you can buy in 'gallon bottles for a dollar' whereas ladies wear 'delicate scents that intoxicate the senses', etc, etc.