No, it is completely out of date. I grew up in the 1950s and I have never heard it used. Never. Never. I've read about it in books. It was popular slang in the "Jazz Age," the 1920s. Don't try to use it. It would sound ridiculous. ADDED: I remember where I heard it. There is a musical, "The Music Man," set in a small town in Iowa in 1912. In a famous bit of song and dialog, a character warns parents about the terrible things happening to the youth of River City: "Mothers of River City, heed that warning before it's too late! Watch for the telltale signs of corruption! The minute your son leaves the house, does he rebuckle his knickerbockers below the knee? Is there a nicotine stain on his index finger? A dime-novel hidden in the corncrib? Is he starting to memorize jokes from Captain Billy's Whiz-Bang? Are certain words creeping into his conversation? Words like 'swell' and 'so's your old man'? If so my friends, ya got trouble!" So this is slang that was becoming popular in the US in 1912.

Hmmm.... Where did you find this? A Google Ngram search shows that it is a rare expression and was most common in the 1920s in American English. A search doesn't find it for British English. I have never heard it during 50 years in the U.S. https://books.google.com/ngrams/graph?content=so%27s+your+old+man&year_start=1800&year_end=2000&corpus=17&smoothing=3&share=&direct_url=t1%3B%2Cso%20%27s%20your%20old%20man%3B%2Cc0