Concerning The Great Gatsby, one would need evidence to suggest that the phone calls from Chicago are a ruse. One would also want concrete motivation for Gatsby wanting to put on a ruse like that.
But in fact, the evidence suggests otherwise. Most importantly, Gatsby is as silent about his work as he can be. In short, he maintains a low profile. His profile is so low that critics have argued about what his business really is. He is likely a bootlegger, but he downplays his business.
Also, Gatsby impresses people through indirect means: his lavish parties and his shirts, which he shows Daisy, are two examples. Personally, he is quite unassuming and shy. Pretending to receive business calls to impress others probably isn't Gatsby's style and is unnecessary.
Finally, it is reasonable and logical that Gatsby owns/runs a business of some kind. His mansion, parties, etc., demonstrate a more than substantial income. Therefore, his receiving a phone call or two should not raise suspicions of his creating a ruse.
Unless you can point to some concrete evidence suggesting the phone calls are fake, the idea doesn't seem to fit the novel.